DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2017

Control Strategy Investigation for a Down- Scaled Forwarder Refinement, Testing and Analysis

ANQING DUAN

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

Examensarbete MMK 2016:99 MDA 571

Control strategy investigation for a down-scaled forwarder

Anqing Duan Godkänt Examinator Handledare 2017-06-15 Jan Wikander Lei Feng Uppdragsgivare Kontaktperson Skogforsk Olle Gelin

Sammanfattning Den dominerande metoden för att skörda träd i Norden är kortvirkesmetoden. Kortvirkesmetoden realiseras av två maskiner: en skördare som används för avverkning av träden och en forwarder som används för att transportera stockarna till en väg som är tillgänglig för lastbilar. För att öka produktiviteten är en möjlig lösning att öka forwarderns körhastighet. Detta kommer dock att bidrar till att operatören utsätts för större vibration och att marken utsätts för större däcktryck. För att lösa ovanstående problem har en sexhjulig forwarder med hjulupphängning i pendelarmar tidigare utvecklats där varje hjul styrs individuellt av en motsvarande hydraulmotor. Med tanke på att genomförande av fälttester på den verkliga forwardern skulle bli tids- och resurskrävande, har tidigare en 1: 5 nedskalad forwarder tillverkats för att underlätta forskningen. På grund av storleksbegränsningarna ersattes de hydrauliska motorerna med linjära cylindrar samt gjordes en del andra konstruktionsändringar. Arbetet med denna avhandling är att ytterligare förfina den nedskalade forwardern med fokus på en 3D modellerings- och animeringsmiljö. Styrstrategin som föreslås är baserad på kinematik. Den föreslagna regleralgoritmen kan balansera den simulerade nedskalade forwardern genom att lösa ett linjärt optimeringsproblem i realtid. Begränsad av sensorprestanda och filteralgoritmer testas endast en förenklad kinematikreglering i simuleringen och i den verkliga nerskalade forwardern. Det kan ses i simulering att både pitch- och roll-vinklar kan minskas kraftigt även med den förenklade reglermetoden vid körning genom Skogforsks standardprovbana. Stabilitetsanalysmetoden för den nedskalade forwardern diskuteras också i denna avhandling. Huvudbidraget från detta examensarbets består i att en annan synvinkel presenterats jämfört med föregående arbeten när det gäller förslag till nya fungerande styrstrategier.

Master of Science Thesis MMK 2016:99 MDA 571

Control strategy investigation for a down-scaled forwarder

Anqing Duan Approved Examiner Supervisor 2017-06-15 Jan Wikander Lei Feng Commissioner Contact person Skogforsk Olle Gelin

Abstract The predominant method of trees harvesting in Nordic countries is cut-to-length logging (CTL). CTL is realized by two machines: a harvester which is used for felling the trees, and a forwarder which is used for transporting the logs to a road accessible by trucks. To increase the productivity, one possible solution is to increase the forwarder driving speed. However, this will make the operator exposed to larger vibration and cause bigger tire-ground pressure. To solve the abovementioned problems, Skogforsk developed a six-wheel pendulum arm suspended forwarder with each wheel of the forwarder controlled individually by the corresponding hydraulic motor. Given that conducting the field tests on the real forwarder will be time consuming and inconvenient, a 1:5 down-scaled forwarder was manufactured previously to facilitate the research. Due to the size limitation, the hydraulic motors are replaced with the linear actuators besides a few other design changes. The work of this thesis is to further refine the down-scaled forwarder with the focus on implementing the control system. The forwarder is modeled using Sim which provides a 3D animation modelling environment. The control strategy is proposed in a perspective of kinematic control. The proposed control algorithm can balance the down-scaled forwarder orientation by solving a linear optimization problem in real time. Restricted by the sensors implementation and filter algorithms, only a simplified kinematics control is tested in the simulation and the real down-scaled forwarder. It can be seen in simulation that both the pitch and roll angle can be reduced greatly by driving through the Skoforsk standard test track with the simplified control method. Stability analysis method for the down-scaled forwarder is also discussed in this thesis. The main contribution of this thesis will be indicating a different point of view from the previous work in terms of control strategy proposal.

Acknowledgement

First of all, I would like to express my gratitude to Ulf Sellgren and Skogforsk rep- resentatives, without whom I will not be able to have this great thesis opportunity.

Second, I really appreciate the guidance from my supervisor Lei Feng. In addition to technical details, I think the most important thing I have learned from him is rigorous working attitude towards research. I would also like to thank Staffan Qvarnström for his help on the hardware.

Last but not least, I am really thankful for the support from my colleagues Yuchao Li, Zhen Li and Qingxiao An. I will never forget the days when we worked together.

Nomenclature

Abbreviations

Symbol Description WAAV Wheeled actively articulated vehicle LQ Linear quadratic LQG Linear-quadratic-Gaussian PID Proportional–integral–derivative MPC Model predictive control IMU Inertia measurement unit PD Proportional–derivative RMS Root-mean-square ECU Electronic control unit FR Front right FL Front left MR Middle right ML Middle left BR Back right BL Back left CoM Center of mass 10 Contents

1 Introduction 1 1.1 Background and Problem Description ...... 1 1.2 Purpose ...... 2 1.3 Delimitations ...... 4 1.4 Method Description ...... 4 1.5 Expected outcomes ...... 5

2 Frame of Reference 7 2.1 Suspension Systems ...... 7 2.2 Brief Survey on Active Suspensions ...... 9 2.3 Wheeled Actively Articulated Vehicle ...... 9 2.4 Vehicle Model ...... 12 2.4.1 Dynamic Model ...... 12 2.4.2 Kinematics Model ...... 14 2.4.3 Model Environment ...... 17

3 Modelling Approaches and Control 19 3.1 Simulation Model ...... 19 3.1.1 Linear Actuator ...... 19 3.1.2 Pendulum Arm ...... 21 3.1.3 Test Track ...... 21 3.1.4 Wheel-Track Interaction ...... 22 3.2 Control Strategy Proposal ...... 23 3.2.1 Kinematic Control ...... 23 3.2.2 Simplified kinematic control: On-off Strategy ...... 26 3.2.3 PID Control ...... 28 3.3 Simulation results ...... 31 4 Implementation 35 4.1 System Overview ...... 35 4.2 Hardware List ...... 36 4.3 IMU Filter Algorithm Analysis ...... 38

5 Results 41 5.1 Simulation results ...... 41 5.1.1 Tilt Angles ...... 41 5.1.2 Tire Pressure ...... 43 5.2 Model verification ...... 49

6 Future Work and Recommendations 53 6.1 Faced Troubles ...... 53 6.2 Future Work ...... 54

Bibliography 57

Appendices Chapter 1

Introduction

This chapter introduces the background of the thesis work, describes the problem to be solved, states the purpose and delimitations, and proposes the selected method as well as the expected outcomes.

1.1 Background and Problem Description

The predominant harvesting method used in Scandinavian countries is cut-to-length logging (CTL), which is based on a two-machine solution: a harvester and a for- warder [1]. The harvester is used for felling, delimbing and bucking trees while the forwarder carries the logs from the harvesting area to a roadside loading area where they can be picked up by a truck.

In order to stay competitive, the Swedish logging industry needs to increase the productivity by 2% to 3% per year [2]. One main solution to improving the produc- tivity is to increase the forestry vehicle driving speed. However, if an off-road vehicle drives through a rough terrain at a high speed, the operator will be exposed to a strong vibration. It has been shown that individual lifetime exposure to the whole- body vibration may play an important part in the evaluation of health effects [3]. In addition, forestry machines are usually very heavy, the usage of them may harm the fragile and irreplaceable landscapes, leading to erosion and soil compaction, which then will affect water absorption and soil permeability [4].

In an endeavor to solve these problems, Skogforsk [5], the forest research institute of Sweden, has built a full-scale forwarder prototype called XT28 as shown in Fig. 1.1. This prototype uses hydraulic pendulum arm suspension for each of its six wheels. The pendulum arm suspension can be controlled individually to drop and lift its corresponding wheel. Therefore, the off-road vehicle will be leveled when driving through the rough terrain with bumps or pits. By doing so, the operator should have better driving comfort since the vehicle can balance itself. Also, the soil damage will be reduced by actively distributing tire-ground pressure among six wheels.

1 CHAPTER 1. INTRODUCTION

Figure 1.1: XT28 Prototype To facilitate the research on the XT28 prototype, a physical 1:5 downscaled for- warder (Fig. 1.2) was realized previously [6]. With the help of the down-scaled prototype, it is much more economic and time saving to test specific features or functions instead of driving a full-scaled version. Some relevant experiments have shown how a scaled vehicle system can be used to facilitate the prototyping of vehicle control systems [7].

Figure 1.2: Down-scaled Prototype 1.2 Purpose

The general context of this thesis work is to further refine the down-scaled forwarder which has been developed previously, yet without any control system implemented. The specific purpose of this thesis work is to investigate a suitable control strategy and manage to implement it on the down-scaled forwarder so that the active sus- pension system would function to keep the vehicle body as horizontally stable as

2 CHAPTER 1. INTRODUCTION possible while reducing the tire-ground pressure. The control effects of the proposed control strategy shall be verified by driving the down-scaled forwarder through the Skogforsk standard test track. The specification of the test track is shown in Fig. 1.3.

Figure 1.3: Skogforsk Test Track Sketch To illustrate the vehicle dynamic behaviour, the coordinate system and naming convention are introduced in Fig. 1.4 from [8].

Figure 1.4: Vehicle Coordination System Based on the abovementioned, the research question of the thesis is formulated as:

How to control a down-scaled forwarder so that it can beep balanced when driving through a test track?

To answer the research question, this thesis should not only adapt and advance the previous control method used on the full-scale forwarder but also prove their utility on the down-scaled version with real experiments. Especially model check will be prioritized since it has never been conducted before while it serves as the foundation that the following control system implementation will base on.

3 CHAPTER 1. INTRODUCTION

1.3 Delimitations

Considering the limited time and the complexity of the project, there are some inevitable limitations to be defined so that it is reasonable to reach the final goals and the bottom line of the project will be secured.

For the vehicle dynamic behaviour improvement, the only coordinates to be im- proved are pitch and roll axis. The test environment is restricted to the Skogforsk standard test track and the driving speed is set to be a constant value. Also, the control system to be implemented in practice would only be the one with the best performance in simulation. It should be noted that the down-scaled forwarder handed over to us has one wheel malfunctioning, which may not be a problem in model simulation but could affect real implementation.

When building the forwarder model, some assumptions are made to keep the model simplified but without the loss of validity. The sensors used in simulation are con- ceived to be sufficiently precise without any noise considered although in reality they are not. Similarly, the linear actuator model is conceived ideal as well, i.e. from voltage input to the displacement output is an ideal integrator regardless of load interruption which can be compensated by required current in the circuit. For the full scaled forwarder, the steering joints of separate vehicle parts are rigid. However, due to the structure deficiency and chosen materials properties, the steering joints of the down-scaled forwarder are pliable, which implies that when going through the tough terrain, tilt degree of the vehicle would be absorbed by the flexibility of the steering joints to some extent. While in the down-scaled forwarder model, the steering joints would be still considered rigid. In addition, since there will not be any model parameter identification conducted, the parameter values used in the model are chosen within the usual range.

1.4 Method Description

The work procedure of this thesis will follow the general V-model. Verification and validation play an very important role in progressing the project. The very beginning task of the project following the literature review is to build the down- scaled forwarder model. This process includes selecting a proper model environment, making reasonable assumptions and considering to set convenient interfaces for the subsequent proposed control systems.

With the chosen model environment, the built model should be as concise as possible but without the loss of necessary accuracy. Model checking will be conducted once the model is finished. Two sets of data from model simulation and real experiments should coincide with each other within allowable deviation. If model checking man- ifests the model is not trustful enough, the model will be rebuilt or fixed until the model is usable, so building model is an iterative process. This is to make sure that

4 CHAPTER 1. INTRODUCTION the control system can be implemented on a reliable model since it is assumed to be time consuming and difficult to fix the model and adapt the control systems in the meanwhile.

Until an acceptable model is built, different control strategies would not be tested in simulation. The testing order had better start with the easiest one. After evaluating their control performance quantitatively, the one with the best performance will be chosen to be implemented on the real down-scaled forwarder, where related hardware will be prepared and deployed. The final result will be compared with the simulation and the conclusion will be drawn.

Due to the potential hardware restriction, the bottom line of this project would keep emphasis on building the model and control strategies comparison in simulation.

1.5 Expected outcomes

To reach the purpose of the thesis work, the following items shall be achieved ac- cordingly as the expected outcomes:

• Building the downscaled forwarder model in Simscape Mulitibody.

• Investigation, simulation and evaluation of different control strategies.

• Model validation by comparing the simulation results with the empirical data.

• Implementing the selected control strategy in practice.

• Documentation of the project.

5 CHAPTER 1. INTRODUCTION

6 Chapter 2

Frame of Reference

This chapter supplements the research background to the thesis further in a detailed way and shows literature review results including theoretical knowledge and engi- neering techniques. Innovations of the thesis will be based on the frame of reference.

2.1 Suspension Systems

Vehicle suspension systems basically consist of tire, spring, shock absorber and link- ages to transmit and filter all forces between body and road [9]. The spring is used to carry the body-mass and isolate the body from road disturbances, which will contribute to ride comfort. The damper is the damping of body and wheel oscilla- tions, where the avoidance of wheel oscillations directly refers to ride safety. Since the vehicle suspension system is responsible for ride comfort and safety, it plays an important role in modern vehicles [10].

Generally speaking, suspension systems can be categorized into passive suspensions, semi-active suspensions, and active suspension systems. A passive suspension has no source of energy. An active suspension incorporates extra energy sources to refine the compromise. The idea of a semi-active suspension is to replace active force generators with continually adjustable elements which can vary or shift the rate of energy dissipation in response to an instantaneous condition of motion [11].

The suspension type used on the down-scaled forwarder is active suspension. It is widely accepted that an active suspension system is an effective way to improve suspension performance. The abstract structure for general active suspension system is shown as Fig. 2.1.

7 CHAPTER 2. FRAME OF REFERENCE

Figure 2.1: Active Suspension Sketch for A Quarter-Vehicle Model

Fig. 2.2 shows the active suspension system structure used on the forwarder. The energy source is supplied by the hydraulic actuator. The left hub is fixed to the vehicle body frame and is free to rotate. The right hub is attached to a wheel and the wheel can move in an arc curve. In total the forwarder has six of this module.

Figure 2.2: Pendulum Arm System

For the down-scaled version, all the components remain the similar structure except that they are realized in a down-scaled size. Due to the size problem, it is not viable to use a down-scaled hydraulic actuator anymore. Therefore, the hydraulic actuator is replaced with a linear actuator which can also allow the stroke to move in a linear way. It should be expected that by doing such modification, the two suspension systems could have two different working principles in that the control signals have different physical meaning. For the active suspension of the full-scaled forwarder, the control signal is given as force, i.e. the wheel will rotate under the exerted force by the hydraulic piston regardless of its position. While for the down-scaled forwarder, the control signal is given as position, i.e. the rotation of the wheel is subject to the position of the piston. Theoretically, the linear actuator can offer enough support force due to its natural self-lock mechanism. If the wheel forces the piston to move backwards, the linear actuator would be damaged. In fact, the external force on the wheel can not even reduce the piston speed lower than the speed at the maximum thrust. The obviously different properties of the two control signals will influence the control system greatly.

8 CHAPTER 2. FRAME OF REFERENCE

2.2 Brief Survey on Active Suspensions

Active suspension control strategies investigation is a very popular topic that a variety of research has been conducted on. Many existing control strategies have been proven to be applicable for active suspension control using quarter-, semi- or full vehicle models.

Krtolica et al. managed to use optimal control to control active suspension system by completing an analytical solution of the related fourth-order LQ problem based on a half-car model [12]. Rao et al. presented a novel fuzzy-logic-based control using a new look-up table for the rule base of fuzzy logic for the vehicle-active suspension of a quarter car [13]. The proposed fuzzy logic controller can enhance comfort in riding faced with uncertain road terrains by reducing the vehicle vibration and dis- turbance considerably. Yamashita et al. used H∞ control theory for a full vehicle model to achieve robust performance and their closed-loop system has been evalu- ated in shaking and driving experiments [14]. Alleyne designed a nonlinear adaptive controller for the active suspension where a standard parameter adaptation scheme, based on Lyapunov analysis, is introduced to reduce the error in the model since the controller relies on an accurate model of the suspension system [15]. Mehra et al. used model predictive control and preview information for the active suspen- sion, manifesting that MPC controller performs better than LQG and is tolerant to significant amounts of noise on the preview information [16].

2.3 Wheeled Actively Articulated Vehicle

In addition to the perspective of controlling the down-scaled forwarder by treating the pendulum arms as active suspension, there are also evidences showing that the down-scaled forwarder behaving quite similar to a wheeled actively articulated vehicle [17]. Some of the typical wheel leg robots are studied as well.

Bill Ross at the Robotics Institute at Carnegie Mellon built an agile six-legged work robot as Fig. 2.3. The robot has high power density and can work in tight and complex space by being equipped with diesel-electric hybrid drive. All six legs have independent wheel drive motors which can help the robot operate in even the most challenging environments [18].

9 CHAPTER 2. FRAME OF REFERENCE

Figure 2.3: Agile Six-Legged Work Robot Fig. 2.4 shows another wheel leg robot named Hylos robot. A combined posture and trajectory control allows to specify the locomotion task in terms of: first the path tracking control and secondly the posture reconfiguration control based on the inverse velocity model of the vehicle [19]. The robot is capable of reducing the pitch and roll angle when running through the inclined ground.

Figure 2.4: Hylos Robot The Jet Propulsion Laboratory planetary rover family is a widely recognized family of passive leg-wheel platforms, for example, the Rocky 7 Rover shown in Fig. 2.5. The Rock 7 Rover is capable of long traverses, autonomous navigation, and science instrument control. The rover has a steerable wheel at the end and a smaller rocker at the other end. A lever can constrain the motion of the main rockers with its two ends attached to the main rockers. This design can provide an important characteristic: one wheel can be lifted vertically while other wheels remain in contact with the ground [20].

10 CHAPTER 2. FRAME OF REFERENCE

Figure 2.5: the Rocky 7 Rover A planetary rover named NEXUS from the Tohoku University is shown in Fig. 2.6. It has 6 wheels connected by a Rocker-Bogie type suspension link system. The modelling of the rover is based on the tire-soil mechanics and the motion dynamics of the vehicle load. Especially the traction factor, which is the ratio of the tangent and normal forces on a tire is derived in [21].

Figure 2.6: NEXUS Fig. 2.7 shows locomotion concept of CRAB consisting of two parallel bogies linked with an articulated rocker. An overview of the software tools that can be used for performance evaluation of all-terrain robots and the performance optimization tool (POT) is introduced in [22]. The performance of the CRAB is evaluated with the proposed POT.

11 CHAPTER 2. FRAME OF REFERENCE

Figure 2.7: CRAB at ETH 2.4 Vehicle Model

Building the model of the object to be controlled always plays an important role in the control strategies investigation. Proper mathematical model should be concluded which can reflect input-output relationship as realistic as possible with reasonable model complexity. Consequently, model environment would be chosen accordingly.

To start with, a proper mathematical expression would be derived for the down- scaled forwarder. There are two viewpoints from which the mathematical model can be derived: dynamics model and kinematics model.

2.4.1 Dynamic Model

The dynamic vehicle model will be built according to the Newton’s second law. Different from prevalent vehicle model where vehicle dynamic behaviour is driven by the forces from active suspension system composed of mass, damper, spring and external actuators, in this project, only the ground-tire force is considered as the factors causing the vehicle dynamic behaviour in that the suspension system of the down-scaled forwarder is quite rigid and multibody system can then be simplified as a whole rigid body except the tires.

The tire-road interaction dynamnics can be achieved by magic formula [23]. Its general form is expressed as

Fx = f(k, Fz) = FzDsin(C · arctan[Bk − E[Bk − arctan(Bk)]]) (2.1) where B, C, D and E are dimensionless denoting stiffness, shape, peak and curvature; Fx the longitudinal force; Fz the vertical force and k the wheel slip. The slope of f at k = 0 is BCD · Fz.

12 CHAPTER 2. FRAME OF REFERENCE

Figure 2.8: An Articulated Vehicle Sketch Similar to [21], equation of motion depicting an articulated model as Fig. 2.8 but without considering steering part is given in Eq. 2.2.

    v˙0 F0 ω˙ 0 N0 T H  ¨  + C =   + J Fe (2.2) θs  ns  ¨ θw nw where

H : inertia matrix for the entire system composed by the inertia property of each body C : non-linear velocity-dependent term v0 : translational velocity of the base body

ω0 : rotational velocity of the base body

θs : suspension angle

θw : rotational angle of the wheel T F0 =(0, 0, −m0g) : forces exerting on the base body

N0 : moments exerting on the base body ns : torque on the suspension joints nw : driving torque of the wheels J : Jacobian matrix T T Fe =(fw1, ..., fw6): tire forces

13 CHAPTER 2. FRAME OF REFERENCE

2.4.2 Kinematics Model

When a mobile robot has active revolute or prismatic joints, it should be considered to build a kinematics model. An assumption here is that the wheels or legs make point contact with the ground.

2.4.2.1 General Kinematics Reconfigurability

The goal of kinematic reconfigurability is to improve robot performance by modi- fying the robot joint variables to optimize a user-specified performance index [24]. Kinematic reconfigurability can be devided into two cases: internal reconfigurability and external reconfigurability.

In internal reconfigurability the link-terrain contact points remain fixed relative to the terrain during the reconfiguration. When it comes to a wheeled robot, the wheel should keep actively controlled without rolling. The mobility of internally reconfigurable robot can be calculated by the Grubler mobility criterion:

j X F = 6(L − J − 1) + fi (2.3) i=1 where j is the number of joints, l is the number of links including the ground, and fi is the number of constraints for each joint i. The terrain profile does not influence the reconfiguration process of an internally reconfigurable robot. Therefore, only using the knowledge of robot kinematics is enough to formulate an optimization problem and a globally optimal solution is possible to find.

In externally reconfigurability the link-terrain contact points will move relative to the terrain during the reconfiguration process. Mobility analysis of an externally reconfigurable robot is different from that of an internally reconfigurable robot. Wheel-terrain contacts must be treated as higher order pairs. Since the reconfigura- tion process involves terrain profile, a globally optimal solution will not be possible to find without knowing the terrain profile. However, the local wheel-terrain con- tact angle can be estimated. An optimization problem can be formulated with a constraint that the reconfiguration process only results in small displacement of the contact points with respect to the terrain.

On-line kinematic reconfigurability has three steps in an ad hoc order:

• Evaluation of the robot configuration denoted with pitch and roll, wheel- terrain contact angles as well as joints position using on-board sensors.

• Computation of a kinematic configuration which can optimize a given perfor- mance index.

• Motion from the current robot configuration to the optimal configuration.

14 CHAPTER 2. FRAME OF REFERENCE

2.4.2.2 Stability Analysis

The control of robotic system under stability margin condition was mainly addressed in the field of legged locomotion. Different mechanical stability margins were defined during past research on walking machines. It can be considered that roughly six tumble stability criteria for walking vehicles were proposed as follows [25]:

1) "Stability Margin": It evaluates the distance between the projection of the center of gravity on the ground and the border of the polygon formed by the supporting feet of the walking vehicle on the plane.

2) "Tumble Stability Margin": When the walking vehicle tumbles around the line connecting two support feet, it evaluates the absolute value of the moment divided by its weight which generates around the line to avoid tumbling. It corresponds to the "Stability Margin" ignoring the dynamic effect when the walking vehicle is on the level ground.

3) "Gradient Stability Margin": It evaluates the inclination of the walking vehicle at which it starts tumbling owing to gravity, when it gets inclined little by little from the level ground.

4) "Tipover Stability Margin": It is similar to the criterion of the "Gradient Stability Margin," but all the external forces including gravity are considered to work on the center of gravity of the walking vehicle.

5) "Energy Stability Margin": In the process of tumbling, the center of gravity passes over the point at which it possesses the maximum potential energy under the field of gravity. This criterion evaluates the stability by the magnitude of the difference between its maximum potential energy and its initial one.

6) "Dynamic Energy Stability Margin": It is similar to the criterion of the "En- ergy Stability Margin," but all the external forces including gravity are con- sidered to work on the center of gravity of the walking vehicle.

In particularly, details about the "Stability Margin" is reviewed here since it is persistent to the down-scaled forwarder and easy to realize [26]. To illustrate, a general mobile robot is defined as Fig. 2.9. The robot has m wheel-terrain contact points pi with i = 1, ..., m numbered in ascending order in a clockwise when viewed from above. The lines joining the terrain-contact points are referred to as tipover th axes and denoted ai, where the i tipover axis is given by:

ai = pi+1 − pi, i = {1, ..., m − 1}, (2.4)

am = p1 − pm. (2.5)

Tipover axis normals li that intersect the center of mass can be described as:

T Ii = (1 − aˆiaˆi )pi+1, (2.6)

15 CHAPTER 2. FRAME OF REFERENCE where aˆ = a/ k a k. Stability angles can then be computed for each tipover axis as the angle between the gravitational force vector fg and the axis normal li:

−1 ˆ γi = σicos (fg · Iˆi), i = {1, ..., n}, (2.7) with ( ˆ +1, (Iˆi × fg) · aˆi < 0 σi = (2.8) −1, otherwise

The overall vehicle stability angle is defined as the minimum of the i stability angles:

α = min(σi), i = {1, ..., n}. (2.9)

When α 6 0 a tipover instability is occurring. Thus, the goal of stability-based kinematic reconfigurability is to maintain a large value of α. It should be noted that when there is applied forces such as a manipulator on its environment, the stability calculation should take external force into account.

Figure 2.9: Stability Definition Diagram 2.4.2.3 Kinematic Control

A kinematic control approach is proposed in order to modify the robot configuration and relocate its center of mass to enhance the system mobility [27]. The idea of the kinematic control is to send command in terms of robot joints velocity to adjust the contact points. Without loss of generality, assuming that the proposed control only actuates in the vertical component of each contact point, the differential kinematics of a robot with 1 DOF for leg is given by: ˙ vzi = jzi (θi)θi (2.10)

where vzi is the linear velocity of the contact point along vertical direction, jzi the vertical component from the system Jacobian matrix, which can be obtained from ˙ the forward kinematics of the mechanism, θi the position and θi the velocity of the

16 CHAPTER 2. FRAME OF REFERENCE

˙ joint i. Considering θi is the control input ui, the following control law can be proposed: −1 ui = jzi (θi) vzci (2.11) where vzci is the commanded linear velocity in the vertical axis of the contact point.

The control law vzci can be calculated from the following objectives:

Ground Clearance Control

The control law should guarantee the ground clearance by following a given reference considering the robot is more stable when it is closer to the ground but should also remain a minimum safety reference.

Orientation Control

The control law should cancel pitch and roll angles and keep the robot body in the horizontal plane.

Traction Control

The control law should distribute the load forces evenly among all wheels.

Stability Control

The control law should maximize the stability of the robot in terms of some stability criterion such as stability margin.

Multiple Objectives Control

The control law can be given to meet multiple objectives stated above by combining the different joint commands.

2.4.3 Model Environment

For vehicle dynamic analysis, there are several modelling platforms. For instance, Adams is a popular multibody dynamic simulation software equipped with Fortran and C++ numerical solvers [28]. It has several advantages including a user friendly graphical user interface (GUI), automatic assembly of Equations of motion and a robust and efficient integration algorithm for differential equations. The Adams software uses generalized Cartesian coordinate and hence the assembled equations are a set of differential algebraic equation of index three [29]. There are also some other vehicle dynamic modellling software such as CarSim [30] and veDYNA [31].

Another powerful modelling software is Matlab. It is possible to realize a state space model using Simulink. And there is previous work realizing a state space model for the forwarder [32]. Also, it is possible to use Simscape/multibody in Matlab environment for the model simulation. Similar model was built with the first generation Simmechanics [33].

17 CHAPTER 2. FRAME OF REFERENCE

Given that it is needed to implement control system for the down-scaled forwarder at a later phase, the interface between Adams and Matlab will be required. Therefore, it will be more convenient to build the model in Matlab directly. In addition, a state space model will not be chosen since it can only reflect continuous behaviour of a dynamic system. The wheels of the forwarder could lose contact with the test track easily. This hard non-linearity property makes linear model, such as state space model, not feasible anymore. Thus the best choice would be building a 3D model using Simmechanics. The newest second generation of Simscape is chosen as the modelling environment.

18 Chapter 3

Modelling Approaches and Control

This chapter presents the insights on the proposed simulation model by showing the model methods for the key components of the forwarder. Some important specifi- cations on the forwarder are also given in this chapter.

3.1 Simulation Model

The down-scaled forwarder model is realized by MATLAB/Simscape MultibodyTM. MATLAB/Simscape Multibody can provide an automatically generated 3-D anima- tion so that the built simulation model can be visualized. This is especially helpful to analyze complex dynamic systems such as robots, vehicle suspensions, construction equipment etc.

3.1.1 Linear Actuator

The real linear actuator is shown as Fig. 3.1 and the related data specification is as Appendix.

Figure 3.1: Linear actuator

The Simulink model blocks layout and its animation result for the linear actuator model are shown in Fig. 3.2.

19 CHAPTER 3. MODELLING APPROACHES AND CONTROL

(a) Simscape Blocks layout

(b) Animation result

Figure 3.2: Linear actuator model The input-output for the linear actuator are the voltage and the stroke speed re- spectively. The ideal relationship between the input and the output is linear with the limitation of maximum voltage 24 V versus maximum stroke speed 15 mm/s. The model scheme as well as its simulation results are shown in Fig. 3.3. The ideal relationship should be linear when the load force is within maximum allowable static force. Disturbances from the external load force variation will be compensated by the current.

Figure 3.3: Ideal linear actuator input-output relationship

20 CHAPTER 3. MODELLING APPROACHES AND CONTROL

3.1.2 Pendulum Arm

The suspension system is composed of six pendulum arms with each one bridging the vehicle body and one wheel. There are two types of pendulum arms due to symmetry. We can take one for example as shown in Fig. 3.4.

(a) CAD model

(b) Simscape animation

Figure 3.4: Pendulum arm suspension system The density value of the material in the simscape model is chosen considering the weight of the linear actuators as well as the steel pendulum arm and hubs. The bearing used in the real model is realized by the joint block between the compo- nents. The maximum velocity and stroke limit position of the piston is saturated in accordance with the real linear actuator.

3.1.3 Test Track

Skogforsk uses standard test track as shown in Fig. 3.5 to test the suspension performance of the forwarder. In order to save computation power, only part of the test track is modeled since the eliminated part is highly repetitive. In fact, there are only three types of bumps sharing similar shape but with different sizes. The sketch of the modeled test track road profile is as shown in Fig. 3.6. The bump width is wide enough to hold the wheels at each side. The bump dimension can be obtained from the coordination which is calibrated in mm.

21 CHAPTER 3. MODELLING APPROACHES AND CONTROL

Figure 3.5: Skogforsk standard test track

Figure 3.6: Test track bump profile 3.1.4 Wheel-Track Interaction

The wheel and track interaction is realized by Simscape Multibody Contact Forces Library [34]. The selected basic elements for representing the interaction between the wheels and the test track are sphere-plane block and sphere-tube block. Sphere- plane block is responsible for the interaction between the wheel-ground and wheel- bump slope. Sphere-tube block is responsible for the interaction between the wheel and the bump peak.

The sphere to sphere contact force block diagram with its specification is shown as Fig. 3.7. For diemnsions, the sphere radius and follower radius are required to be set. For contact, contact stiffness and contact damping are parameters to be set. For coefficient of kinetic friction and coefficient of static friction as well as velocity threshold are required to be set.

22 CHAPTER 3. MODELLING APPROACHES AND CONTROL

Figure 3.7: Contact Force Block Mask 3.2 Control Strategy Proposal

The control strategy proposed for the down-scaled forwarder active suspension sys- tem should take linear actuator characteristics into consideration. Since the selected linear actuator has a highly linear property between the input voltage and the output stroke speed, it can be controlled comparatively easily. Advanced control strategies used for the real forwarder active suspension system composed of hydraulic cylin- ders could be deprived. To start with, kinematic control as mentioned in the above section would be tried firstly.

3.2.1 Kinematic Control

There are two purposes for the kinematic control: 1) keep the forwarder in horizontal balance so that the driver can feel comfortable; 2) make sure that the number of the wheels that are in contact with the ground is as big as possible. Before implementing kinematic control, there are some assumptions made:

Assumption 1 : The wheel-terrain contact is point contact.

Assumption 2 : Wheel-terrain contact angle keeps constant when the forwarder is driving or moving its joints.

Assumption 3 : There is no slip between the wheel and the terrain.

Assumption 4 : There are always at least three wheels in contact with the ground.

23 CHAPTER 3. MODELLING APPROACHES AND CONTROL

To illustrate the proposed kinematic control method, a sketch of the forwarder with associated frames is shown in Fig. 3.8. The velocity expression is denoted with its reference frame on the super script:

• Ro: the reference ground frame or world frame

• Rf : the main forwarder platform frame attached to the center of gravity

w • Ri : the ith wheel frame without rotation attached to the wheel center

The linear actuator piston position for each wheel is denoted as li and the rolling angular velocity magnitude for each wheel with respect to the world frame is denoted o o as ωri , i = {1, .., 6}. The ith tire-terrain contact angle in the vertical plane is αi . f The ith pendulum arm angular velocity ωi with respect to the forwarder reference frame is expressed as f ˙ ωi = Ji(li)li (3.1) where Ji is the Jacobian matrix for the ith wheel. The vertical component of the o pendulum arm end point on the vehicle body side vzi with respect to the world frame o reference is of interest since it contributes to the forwarder orientation directly. vzi is a linear combination resulting from two parts: contact points vertical movement o w vczi and pendulum arm end point vertical movement vpzi due to the pendulum arm rotation and the pitch and roll angle of the forwarder:

o o w vzi = vczi + vpzi (3.2)

The contact points movement vczi can be calculated with wheel rolling speed and tire terrain contact angle.

f R

O z 4

RO w 5 Ri yO 2 O 1 6 3 xO

Figure 3.8: Sketch of Forwarder with Associated Frames o Before analyzing the effects of vzi on the forwarder configuration, it should be noted that three wheels from both sides are enough to define the orientation of the for- warder. So only three wheels from both sides will be selected to reconfigure the

24 CHAPTER 3. MODELLING APPROACHES AND CONTROL forwarder orientation. The selection criterion is based on tire-terrain pressure value. The wheels with bigger tire-terrain pressure value are preferred since they are con- sidered having bigger chance in contact with the ground during reconfiguration. The wheel in the left side with the maximum tire-terrain pressure is selected and labeled as a. The wheel in the right side with the maximum tire-terrain pressure is selected and labeled as b. The third selected wheel has the maximum tire-terrain pressure value in the remaining wheels. The total reconfiguration of the forwarder is considered a superposition of the three wheels effects.

4 1

2 α 5

β

3 6

Figure 3.9: Top View of the Forwarder The forwarder orientation is expressed with pitch and roll angles. It can be consid- ered a unit vector is fixed upwards perpendicular to the vehicle body so that when there is tilt angle, the projection of this unit vector on the horizontal plane is (α, β) as in Fig. 3.9 where α is roll angle and β is pitch angle. Let labc denote the vector originating from bc with the end point at a. An optimization problem here is to make the forwarder go back to balance as fast as possible, so the cost function is formulated as

o o o − (labc × vza + lbca × vzb + lcba × vzc ) · (α, β) (3.3) with the constraint that the other wheels in contact with the ground should be able to have contact with the ground during reconfiguration:

o o o min(vzj ) 6 vzj 6 max(vzj ) (3.4) o where j indicates the wheel number in contact with the ground, vzj the compliant o o speed as given in Eq. 3.5, min(vzj ) and max(vzj ) are calculated from the linear actuator piston speed range.

o k ljab k o k ljac k o k ljbc k o vzj = sgn(ljab ·lcab) vzc +sgn(ljac ·lbac) vzb +sgn(ljbc ·labc) vza k lcab k k lbac k k labc k (3.5)

25 CHAPTER 3. MODELLING APPROACHES AND CONTROL

The command for the wheels that are in the air should extend the linear actuator so that the wheel can be put down to contact the ground.

3.2.2 Simplified kinematic control: On-off Strategy

On-off control might be the simplest control strategy. It only serves as a negative feedback controller in the system. Like a switch, the control signal operates at two states depending on the sign of the difference of the process variable and the pre-set value. However, it could be cheap and effective in quite some circumstances such as fan controlling or temperature controlling [35].

In our case, on and off represent the two directions for the linear actuator. On-off control strategy is employed due to the following reasons. First, in order to make the pitch and row angle get back to zero at the fastest speed, the linear actuators should operate with fully opened at two directions. This will give the forwarder body the fastest rotation speed. Second, there is no overshoot problem for linear actuator. So there is no worry about unexpected overshoot caused by the full speed. The linear actuator can stop immediately when giving no input voltage. Third, on-off control can be realized easily since it dose not require expensive hardware setup. Control signal cold be computed quickly without unnecessary delay.

Figure 3.10: On-off control system operation scheme However, there could be some other problems caused by using on-off control strategy. A typical problem is chattering problem arising around the set point. When the measured controlled variable crosses the set point, there is danger that the control signal switches on and off at very high frequency. To avoid chattering problem, deadband is usually used in practical on-off controllers. A deadband, as known as hysteresis, is a region around the set-point value in which the controller has no action.

26 CHAPTER 3. MODELLING APPROACHES AND CONTROL

Figure 3.11: On-off control system with deadband When the pitch or roll angle is not zero, the linear actuators should operate ac- cordingly. Especially, when the wheel is off the ground, the corresponding linear actuator should extend and put the wheel down in order to make the wheel contact the ground again regardless of the value of the pitch and roll angle. Each linear actuator operation principles are shown as Table 3.1. Pitch+ represents the front of the forwarder is higher than the rear of the forwarder and for pitch− vice versa. Roll+ represents the right side is higher than the left side and for roll− vice versa. When programming the real controller, there is a set deadband to avoid chatter, so that only the tilt angle exceeds than some value the linear actuators would operate. Table 3.1: Linear actuators operation principle

FL FR ML MR RL RR Off the ground + + + + + + Pitch+ + + − − − − Pitch− − − − − + + Roll+ − + − + − + Roll− + − + − + −

From the table it can be observed that the linear actuator operation direction con- flicts when the sign of the pitch angle and roll angle matches in a specific way. It should be considered to assign weight coefficients for the control signal from the pitch and roll angle respectively. The coefficients should make sure that the most severe situation matters and get the dominance of the linear actuator. Taking the FL wheel as an example, a pseudo control law is given by

27 CHAPTER 3. MODELLING APPROACHES AND CONTROL

( sgn(epitch(t)) × u , |epitch(t)| > Deadband upitch(t) = max pitch (3.6a) FL pitch 0, |e (t)| 6 Deadbandpitch ( −sgn(eroll(t)) × u , |eroll(t)| > Deadband uroll(t) = max roll (3.6b) FL roll 0, |e (t)| 6 Deadbandroll pitch pitch roll roll uFL(t) = KFL uFL (t) + KFL uFL (t) (3.6c)

where umax denotes the maximum control power for the linear actuator to extend at the limit speed; Deadbandpitch Deadbandroll are introduced pre-set deadband value to avoid chattering problem as mentioned previously. The final output control signal pitch uFL(t) is computed as a linear combination of uFL (t) in terms of pitch angle error roll pitch and uFL (t) in terms of roll angle error with corresponding weight coefficients KFL roll and KFL . The control laws of the wheels FR, RL and RR are similar to that of FL. The only difference lies on the sign before the maximum control signal umax.

When it comes to the wheels ML and MR, the control law is a bit different because the linear actuators always need to contract when the pitch angle is not zero despite of its sign. It can be interpreted by considering the forwarder like a seesaw. When the pitch angle is not zero, the middle wheels serving as a pivot should reduce their height. Therefore the linear actuators at the middle wheels should always contract when the pitch angle exceeds the pre-set deadband value. A control law for ML is given in Eq. 3.7 and a similar form applies for MR.

( −u , |epitch(t)| > Deadband upitch(t) = max pitch (3.7a) ML pitch 0, |e (t)| 6 Deadbandpitch ( −sgn(eroll(t)) × u , |eroll(t)| > Deadband uroll(t) = max roll (3.7b) ML roll 0, |e (t)| 6 Deadbandroll pitch pitch roll roll uML(t) = KML uML (t) + KMLuML(t) (3.7c)

3.2.3 PID Control

Based on the linear actuators operation principles table, it is also possible to imple- ment PID controller for the suspension system. Taking the FL wheel as an example, the proposed PID control law are formulated in Eq. 3.8.

28 CHAPTER 3. MODELLING APPROACHES AND CONTROL

Z t pitch pitch pitch pitch pitch pitch pitch de (t) uFL (t) = Kp_FLe (t) + Ki_FL e (τ)dτ + Kd_FL (3.8a) 0 dt Z t roll roll roll roll roll roll roll de (t) uFL (t) = Kp_FLe (t) + Ki_FL e (τ)dτ + Kd_FL (3.8b) 0 dt pitch pitch roll roll uFL(t) = KFL uFL (t) + KFL uFL (t) (3.8c)

The control signal for the FL wheel is uFL(t), which is derived from two parts, the pitch pitch control signal uFL (t) denoting the pitch side with the pitch error e (t) and the roll roll pitch control signal uFL (t) denoting the roll side with the roll error e (t). KFL and roll KFL are the weight coefficients to combine the two control signals. The value of the pitch pitch pitch roll roll roll PID coefficients Kp_FL, Ki_FL, Kd_FL, Kp_FL, Ki_FL, Kd_FL should be selected accordingly. Similarly we can obtain the PID control law for the remaining wheels FR, RL and RR. It should be noted that the sign of the PID coefficients should be decided dependent on the operation principle.

Here the control law form for the wheels ML and MR is different as well. The control law is given separately. Taking the ML wheel as an example, the PID control law is given by ( −u , |epitch(t)| > Deadband upitch(t) = max pitch (3.9a) ML pitch 0, |e (t)| 6 Deadbandpitch Z t roll roll roll roll roll roll roll de (t) uML(t) = Kp_MLe (t) + Ki_ML e (τ)dτ + Kd_ML (3.9b) 0 dt pitch pitch roll roll uML(t) = KML uML (t) + KMLuML(t) (3.9c) where umax denotes the maximum control signal for the linear actuator to extend. A similar control law can be derived for the MR wheel.

All PID control law only applies when the wheels contact the ground. As long as there is clearence distance between the wheel and the ground, the corresponding linear actuator would extend to make the wheel contact the ground again.

Considering the actuator saturates there will be windup in the integrator. In order to avoid windup caused by the integrator of the PID controller, a standard anti-windup technique called back-calculation as in Fig. 3.12 is applied to the PID controller. The difference between the output of the controller u and the actuator output usat is fed to the input of the integrator with gain Kt so that when the actuator saturates, the integrated error will be decreased and the controller output can be kept close to the saturation limit. The feedback gain Kt is responsible for the rate of the controller output reset, with a large value giving a short reset time. But gain Kt cannot be too large since measurement noise can then cause an undesirable reset. A reasonable value for Kt is a fraction of Kd/Kp [36].

29 CHAPTER 3. MODELLING APPROACHES AND CONTROL

Figure 3.12: PID Controller with Anti-windup PID parameters selection is conducted based on a simplified and linearized model where the plant is assumed to behave as an integrator with voltage input and error angle output as shown in Fig. 3.13. It should be noted that the gain of the plant can vary with pitch and roll as well as the change of the support method for the forwarder. It is considered to use roll angle as the index. Roll angle is more critical than pitch since the gravity center projection is closer to the wheels than pitch when suffering the same tilt angle. The value of the gain is expressed as

voltage for linear tilt angle actuator 1 Kv_w s

Figure 3.13: Simplified Model for Plant

∆Cl 0.16 Kv_ω = = rad/s · V = 0.0023rad/s · V (3.10) Vmax × wd × tmin 24 × 0.4 × 7.3 where ∆Cl is the maximum ground clearance difference between the lowest position and the highest position; Vmax is the maximum voltage for the linear actuator; wd is the vehicle width; tmin is the minimum time for the vehicle travel through the maximum ground clearance. In consequence, the block used for tuning the PID parameters is shown in Fig. 3.14. The selected PID and filter value should give minimum overshoot and fast response.

30 CHAPTER 3. MODELLING APPROACHES AND CONTROL

Figure 3.14: Block Used for Tuning PID 3.3 Simulation results

The influence of the PID value on the output is shown as Fig. 3.15. It can be seen that when P = 400 and I = 120 the process is fast but without overshoot. The value of D has no effect on the results and its value is chosen as 10.

0 P = 400 P = 300 -0.1 P = 500

-0.2

-0.3

-0.4

0 5 10 15 20 25 30

Offset=0 (a) P Tuning Process with D = 10 and I = 120

0

I = 120 I = 90 -0.1 I = 150

-0.2

-0.3

-0.4

0 5 10 15 20 25 30

Offset=0 (b) I Tuning Process with P = 400 and D = 10

Figure 3.15: PID Tuning Process

31 CHAPTER 3. MODELLING APPROACHES AND CONTROL

0

D = 10 -0.1 D = 1000 D = 2000

-0.2

-0.3

-0.4

0 5 10 15 20 25 30

Offset=0 (c) D Tuning Process with P = 400 and I = 120

Figure 3.15: PID Tuning Process (cont.) The Simscape model overview is given in the Appendix. To start with, the pistons of the linear actuators are set at the middle position lm. This can make sure that the linear actuators can handle both situations of extending or contracting with the same capability. The forwarder running speed is set at v = 45mm/s to mimic the real forwarder running speed.

The simulation results from on-off control and PID control are given in Fig. 3.16 and Fig. 3.17 respectively. From the animation process, it can be observed that on-off control somehow generates a more swift reaction speed to the bumps than the PID control. This can be explained that on-off control in some cases gives the full power for the linear actuator to operate while the control signal from PID is dependent on the error and thus might not be at its maximum value.

(a) (b)

(c) (d)

(e) (f) Figure 3.16: On-off control animation results 32 CHAPTER 3. MODELLING APPROACHES AND CONTROL

(a) (b)

(c) (d)

(e) (f) Figure 3.17: PID animation results During simulation, the center of mass of the forwarder tends to become higher after it comes through the test track. All the linear actuators extend to its longest state at the end of the simulation. In order to guarantee the center of mass of the forwarder can tend to converge to the level where the linear actuators are at the middle position, another control rule as in is introduced to adjust the height the forwarder body. It should be noted that the control law will only apply when

pitch roll |e (t)| + |e (t)|

( PRR PRR sgn(6lm − i=FL li) × umax, |6lm − i=FL li| > DeadbandCoM ui = 0, else (3.12) where i = FL, FR, ML, MR, RL, RR.

PRR As long as the sum of the extension length of all linear actuators i=FL li) exceeds the threshold denoted by DeadbandCoM , the linear actuators would operate to adjust the forwarder height.

33 CHAPTER 3. MODELLING APPROACHES AND CONTROL

When running simulation, it is observed that the forwarder has an obvious longitu- dinal shock when the front actuators extend to a long distance and the front wheels start to come through a bump. It is because that the a more vertical pendulum arms at the front of the forwarder will have a higher chance to make the front wheels hit into the bump when it rotates according to the pitch error. A diagram explaining this phenomena is as Fig. 3.18. The dashed line represents the motion track of the peak point at the wheel that when the wheel is rotated by the pendulum arm to compensate the pitch error. The longitudinal shock happens because of the inter- section between the dashed line and the bump slope. Actually in this situation it is better to put down the front wheels rather than lift them up although the pitch angle here is positive. When going through the bumps, perhaps whether the front wheels should put down or lift up should be decided by the relative angle of the pendulum arms and the bump slope.

Figure 3.18: Longitudinal shock diagram

34 Chapter 4

Implementation

This chapter describes the technical details of the involved hardware and software for real implementation and elaborates the reasons why they are chosen as such.

4.1 System Overview

Figure 4.1: System overview The overview of the system is as shown in Fig. 4.1. In the system the controller lies on the center place where the measured data is collected and the control signals are computed and sent. The down-scaled forwarder is driven by the EC motors. Each EC motor is controlled by an ESCON speed controller so that they can maintain a constant speed. Current sensors are connected in series with the EC motors so that the load variation of the wheel can be measured. By doing so, it will be known whether the wheel contacts the ground or not. It is expected that the wheel hangs in the air would cause a smaller current in the circuit since the power required to drive an idle wheel is minimum when the input voltage remains constant. In order to obtain the pitch and roll angle, an inertia measurement unit (IMU) is needed to

35 CHAPTER 4. IMPLEMENTATION install on the forwarder. Based on the received data from the sensors, the controller will send control signals to the linear actuators.

All the signals should be filtered with a low-pass filter to filter out additional noise before they are used. The on-board low-pass filter on the Arduino board can be used.

4.2 Hardware List

Involved hardware items are listed as below along with the introductory description on how to set them up.

µ-controller

The chosen µ-controller is Genuino 101 as shown in Fig. 4.2. It is the same prod- uct as Arduino 101 with the exception that it is only available outside the USA. The controller is quite easy to program with open-source code and mature libraries. Genuino 101 can be purchased at an entry-level price. In addition, it has built-in 6-axis accelerometer/gyro on the board. This can be used as IMU in our case. Some relevant technical specifications are as in Table 4.1. Table 4.1: Technical specifications for Genuino 101

Microcontroller Intel Curie Operating Voltage 3.3V (5V tolerant I/O) Input Voltage (recommended) 7-12V Input Voltage (limit) 7-17V PWM Digital I/O Pins 4 Analog Input Pins 6 Clock Speed 32MHz Features Bluetooth LE, 6-axis accelerometer/gyro

At least two controller are required since there are only 4 PWM pins for each con- troller while it is needed to control six linear actuators with each on connected to one PWM pin. When doing real implementation, three controllers are used and put at the front part, rear part and middle part of the down-scaled forwarder separately. A benefit by doing so is that the IMUs can detect the pitch and roll angle at differ- ent parts of the forwarder since the joint between two parts is not rigid enough to consider the whole forwarder as a rigid body.

36 CHAPTER 4. IMPLEMENTATION

Figure 4.2: Genuino 101 Current sensor

The current sensor is ACS714 and its wire connection is as shown in Fig. 4.3. ACS714 operates with input voltage +5V which can be powered by the µ-controller. The output voltage is proportional to AC or DC currents with the sensitivity 185 mV/A. Six current sensors are required to measure the currents for the six wheels.

Figure 4.3: Current sensor H-bridge

Since the linear actuators require very high power to drive. H-bridge are required to drive the linear actuators. Pololu Dual MC33926 Motor Driver Shield for Arduino is used as shown in Fig. 4.4. The maximum operating voltage is 28V is higher than the linear actuator operating range 24V. In addition, there is an Arduino library making it easy to use this motor shield.

Figure 4.4: H-bridge

37 CHAPTER 4. IMPLEMENTATION

Speed Controller

The EC motor to drive the forwarder is controller by the speed controller ESCON as in Fig. 4.5. A more detailed specification can be referred in the datasheet [37]. When programming the controller, some parameters such as motor type, required speed, control method etc. can be deployed by the interface software ESCON Studio as in Fig. 4.6.

Figure 4.5: Speed controller

Figure 4.6: ESCON Studio 4.3 IMU Filter Algorithm Analysis

As mentioned in section 4.2, the built-in IMU on the Genuino 101 board is used. Since the raw data cannot be used directly due to the noises, some filter algorithm shall be designed accordingly. The officially recommended filter algorithm by Ar- duino is Madgwick filter algorithm developed by Sebastian Madgwick [38]. The algorithms generate four quaternions from the raw values of a gyroscope and ac- celerometer. The four quaternions are then used to calculate Euler angles pitch,

38 CHAPTER 4. IMPLEMENTATION yaw, and roll. The advantages of the algorithm are allegedly computationally inex- pensive and efficient even at low sampling rates.

However, in real practice, it was observed that the dynamic angles obtained from the algorithm have a big deviation from the real one by the evidence of a comparison with complementary filter [39] as shown in Fig. 4.7.

150 Complementary 100 Complementary filter functions Madgwick well in spite of sudden change 50 of the angle

0 Accurate angle only Measured angle (Deg) when moving slow -50 for Madgwick filter

-100 0 5 10 15 20 25 30 35 40 45 Time (Sec) Figure 4.7: Filter algorithms comparison A complementary filter calculates the estimated angle by combining the data from both the gyroscope and the accelerometer. An abstract form for complementary filter is as in Eq.4.1.

θest = Kgyr × (θest + gyrData × dt) + Kacc × accData (4.1)

where θest denotes estimated estimated angle and Kgyr and Kacc are weight coef- ficients for the angles calculated from gyroscope data gyrData and accelerometer data accData respectively. From real experience, the coefficients are usually chosen as Kgyr → 1, Kacc → 0 and Kgyr + Kacc = 1.

A detailed explanation is as Fig. 4.8. On the short term, the data from the gyroscope is used because it is very precise and not susceptible to external forces. On the long term, the data from the accelerometer is used as it does not drift.

Figure 4.8: Complementary filter principle

39 CHAPTER 4. IMPLEMENTATION

40 Chapter 5

Results

This chapter presents the results from the simulation as well as the real experiment. For simulation, control effects and comparison of the two control strategies are presented. For the real experiment, because IMU has problem with the pitch and roll measurement, only model verification is given.

5.1 Simulation results

This section show the numerical results from the simulation in terms of tilt angles and tire pressure.

5.1.1 Tilt Angles

Pitch and roll angle under no control and the two control strategies are shown as Fig. 5.1 and Fig. 5.2 respectively. It can be seen that both PID control and on-off control reduce pitch and roll angle errors to a large extent. It seems that on-off control performs better than PID control since it yields a lower pitch and roll peak angle. Also, it is observed that the angle peaks are shifted a bit. it can be explained by the horizontal movement of the wheels when the linear actuators operate. In addition, longitudinal shock can also contribute to the peak shift.

41 CHAPTER 5. RESULTS

Table 5.1: Control effects comparison

R 2 2 R 2 2 Control strategy epitchdt (deg · s) erolldt (deg · s) without control 95.25 275.03 On-off 18.33 16.15 PID 19.45 37.87

3 Without control

2 PID control On-off control

1

0

Pitch (deg) -1

-2

-3

-4 0 5 10 15 20 25 30 35 Time (Sec)

Figure 5.1: Pitch Angle Error

8 Without control 6 PID control On-off control 4

2

0

Roll (deg) -2

-4

-6

-8

-10 0 5 10 15 20 25 30 35 Time (Sec)

Figure 5.2: Roll Angle Error A quantitative comparison between PID control and on-off control effects is given in Table 5.1. The evaluation index is chosen as error square integral. PID can reduce pitch error up to 79.6% and roll angle up to 86.2%. On-off control can reduce pitch angle up to 80.8% and roll angle up to 94.1%. On-off control outperforms than PID control on both pitch and roll angle.

42 CHAPTER 5. RESULTS

5.1.2 Tire Pressure

Tire pressure values of different cases are compared in this section. Tire pressure for each wheel without control, with on-off control and with PID control are shown in Fig. 5.3, 5.4, and 5.5 respectively. It can be observed that there are peaks in the plots. This could result from numerical errors such as long simulation sampling time.

43 CHAPTER 5. RESULTS

700

600

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300

FL Tire Pressure (N) 200

100

0 0 5 10 15 20 25 30 35 40 Time (s) (a) FL pressure

1000

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0 0 5 10 15 20 25 30 35 40 Time (s) (b) FR pressure

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0 0 5 10 15 20 25 30 35 40 Time (s) (c) ML pressure

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200

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0 0 5 10 15 20 25 30 35 40 Time (s) (d) MR pressure

Figure 5.3: Tire Pressure without Control

44 CHAPTER 5. RESULTS

1000

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0 0 5 10 15 20 25 30 35 40 Time (s) (e) RL pressure

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200

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0 0 5 10 15 20 25 30 35 40 Time (s) (f) RR pressure

Figure 5.3: Tire Pressure without Control (cont.)

45 CHAPTER 5. RESULTS

800

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0 0 5 10 15 20 25 30 35 40 Time (s) (a) FL pressure

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0 0 5 10 15 20 25 30 35 40 Time (s) (d) MR pressure

Figure 5.4: Tire Pressure with On-Off Control

46 CHAPTER 5. RESULTS

1000

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0 0 5 10 15 20 25 30 35 40 Time (s) (e) RL pressure

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0 0 5 10 15 20 25 30 35 40 Time (s) (f) RR pressure

Figure 5.4: Tire Pressure with On-Off Control (cont.)

47 CHAPTER 5. RESULTS

800

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300 FL Tire Pressure (N) 200

100

0 0 5 10 15 20 25 30 35 40 Time (s) (a) FL pressure

1000

900

800

700

600

500

400

FR Tire Pressure (N) 300

200

100

0 0 5 10 15 20 25 30 35 40 Time (s) (b) FR pressure

600

500

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300

200 ML Tire Pressure (N)

100

0 0 5 10 15 20 25 30 35 40 Time (s) (c) ML pressure

800

700

600

500

400

300 MR Tire Pressure (N) 200

100

0 0 5 10 15 20 25 30 35 40 Time (s) (d) MR pressure

Figure 5.5: Tire Pressure with PID Control

48 CHAPTER 5. RESULTS

1000

900

800

700

600

500

400

RL Tire Pressure (N) 300

200

100

0 0 5 10 15 20 25 30 35 40 Time (s) (e) RL pressure

1000

900

800

700

600

500

400

RR Tire Pressure (N) 300

200

100

0 0 5 10 15 20 25 30 35 40 Time (s) (f) RR pressure

Figure 5.5: Tire Pressure with PID Control (cont.) The integral of tire pressure over test time is shown in Table 5.2. There is no direct evidence showing that the proposed control strategies can reduce tire-terrain pressure. Traction control should be considered to solve this problem.

Table 5.2: Tire Pressure Comparison

R Ndt (×106Ns) FL FR ML MR RL RR without control 6.7248 2.2162 3.0045 3.0766 6.5346 8.4980 On-off 4.8218 3.9437 6.7591 6.3930 10.286 11.037 PID 4.7083 4.1298 7.2176 5.4023 9.5994 12.106

5.2 Model verification

It can be seen in Fig. 5.6 that the forwarder drives under control can behave accordingly to some extent. The linear actuator contracted when the wheel is on the bump. However, during doing real experiment, the forwarder keeps chattering when the linear actuators operate. Because the IMU cannot measure the angle error

49 CHAPTER 5. RESULTS precisely under dynamic status. The measured data drifts a lot compared with the real value. Therefore, only the forwarder driving through the test track without control are realized. The pitch and roll angle error are then compared with the simulation value for model verification.

(a) Before the Bump

(b) On the Bump

Figure 5.6: Rear Left Wheel under Control Fig. 5.7 shows pitch angle match degree and Fig. 5.8 shows the roll angle match degree. It can be seen that the general trend matches for the both pitch and roll angle. However, when the forwarder drives through the bumps, the IMU measure- ment includes more noise than it is static. In addition, the measured angle becomes smaller gradually. This results from the low rigidity at the forwarder joint when the IMU is placed at the front of the forwarder. When the front wheels are on the ground and the middle and rear wheels are still going through the bumps, the joint of the forwarder absorbs some of the angle error.

3

2 Field test Simulation

1

0

-1

-2 Pitch angle (deg)

-3

-4

-5

-6 -5 0 5 10 15 20 25 30 35 40 Track position

Figure 5.7: Pitch Angle Error Verification

50 CHAPTER 5. RESULTS

8

6 Field test Simulation

4

2

0

-2 Roll angle (degt)

-4

-6

-8

-10 -5 0 5 10 15 20 25 30 35 40 Track position

Figure 5.8: Roll Angle Error Verification

51 CHAPTER 5. RESULTS

52 Chapter 6

Future Work and Recommendations

This chapter presents the troubles faced during the project, the potentials that is worth digging further in the future and the recommendations on this project.

6.1 Faced Troubles

During building simulation model with Simmechanics, some abnormal modeling results happened occasionally. For example, the intersection between the wheel and the ground could increase dramatically suddenly. The model run very slow and a long sampling period had to be chosen to speed up simulation time. Another method to reduce simulation time is to decrease the stiffness of the model since high stiffness will cause high frequency.

A very challenging part in this project is undoubtedly the hardware implementation. Actually the prototype of the down-scaled forwarder used in the project is sort of fragile. When the chattering problem happened to the forwarder, the wheels dropped off from the forwarder body. The awkward moment was captured as Fig. 6.1. Besides the poor connection between the wheels and the pendulum arms, the joints of the different parts of the forwarder are also too soft while for the real full size forwarder it should be very rigid. The high flexibility of the joints makes the measured pitch and roll angle different as IMU installation place changes. When doing real test, there is one EC motor malfunctioning so there is only total of five wheels capable of rotating. In addition, since the bumps are made of steel, they are very slippery. Sometimes the forwarder cannot drive through the bumps and need some extra push.

53 CHAPTER 6. FUTURE WORK AND RECOMMENDATIONS

Figure 6.1: The Fragile Forwarder The battery used to actuate the linear actuators and the EC motors drains too quickly. Normally the battery can only support the experiment for a quite short time and then much time is needed to power the battery again. Otherwise the the linear actuators could not drive the wheels with full speed. This could prevent the consistency of doing the test.

To determine whether the wheel contacts the ground or not, tyre-ground pressure was considered to be the index at the first place. To test tyre-ground pressure value, off the shelf sensor such as tire-pressure monitoring system (TPMS) was considered useful. However, the sensed value is transmitted in an encrypted way. Therefore current sensor was then chosen as the sensor to tell whether the wheel is on the ground or not. However, in the real test, it was found that when the wheel rotates on the ground, the required current to drive the forwarder is too low to sense accurately. And the currents in six wheels are very hard to be distributed evenly. An alternative solution to indicate the wheel state should be proposed.

The IMU always has problem with showing accurate angle value. A main reason can be the selected filter algorithms. As stated earlier, the performance of IMU depends on the filter algorithms greatly. Even though a better algorithm was selected, the measured signal still includes too much noise. When running Matlab to receive the measured data from the sensors, it was observed that the data was not received in real time. So the time scale of the final plot would be different from the real time scale.

6.2 Future Work

Despite of the aforementioned aspects that could be taken care of in the future, there is much space for the new directions of the project. In this thesis work,

54 CHAPTER 6. FUTURE WORK AND RECOMMENDATIONS only pitch and roll angle are considered to be reduced. Other active suspension evaluation index could be included such as vertical acceleration or angle acceleration. Some comprehensive index such as comfort index can also be considered to evaluate suspension control performance. Longitudinal shock as mentioned earlier should be treated seriously. The relative angle composed by the pendulum arm and the bump slope should be employed as control signal for the linear actuators.

Some advanced control strategy should be explored further for the active suspen- sion. A promising method could be compliance control [40]. This might require to implement force sensors for the linear actuators. Although trying some other advanced control strategy, it is inevitable to add new sensors to the forwarder.

55 CHAPTER 6. FUTURE WORK AND RECOMMENDATIONS

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60 Appendices DLA series 50-300 mm 1200 N with potentiometer feedback 132 72 20

12 Ø40 9 Ø8 Ø8 Ø20 30.5 82 20 18 36.7 24

42 L=900 A ±3 mm B ±3 mm Retracted Extracted

MODEL NO. DESIGNATIONS

DLA - VOLTAGE - RATIO - A - STROKE - FEEDBACK - IP65

Example: DLA-12-5-A-50-POT-IP65

ACTUATOR DATA Reduction 5 10 20 30 40 Voltage (VDC) 12/24 12/24 12/24 12/24 12/24 Current at max. thrust (A) 3.0/1.5 3.0/1.5 3.0/1.5 3.0/1.5 3.0/1.5 Max. thrust (N) 200 300 500 800 1200 Static force (N) 1500 1500 1500 1500 1500 Speed at max. thrust (mm/s) 35 25 15 10 5

ACTUATOR STROKE DATA Stroke version B (mm) 50 100 150 200 250 300 Retracted length A (mm) 195 246 297 348 399 450 Resistance (Kohm) 0.3-9.3 0.3-9.7 0.3-8.6 0.3-9.6 0.3-9.3 0.3-9.3 Feedback (ohm/mm) 180 95 55 46 36 30 Life time number single strokes 80.000 40.000 26.666 20.000 16.000 13.333 Weight (g) 1110 1175 1250 1315 1385 1455

ACTUATOR FEATURES AND STANDARD DATA POTENTIOMETER FEATURES AND DATA STANDARD CUSTOMIZATION OPTIONS Type Wire wound Type Electric linear actuator Resistance 0.3 - 9.7 Kohm Motor type Brush PM dc motor Resolution 0.025% Cable Flying wire 900 mm Yes Resistance tolerance ±5% Voltage 12 or 24 volt dc 36 or 48 volt dc Linearity ±0.25% Screw type ACME pitch 3 mm 3+2 leads flying wire Cable Noise level < 60 db (A) Yes 900 mm Life time 4 million mm total stroke Limit switches Integrated non adjustable Stroke length Direction movement By reversing voltage polarity Yes Stroke tolerance ±3 mm ±2 mm Potentiometer wiring Duty cycle 25% Max. duty operational time 1 min. max. thrust YELLOW V input Protection class IP65 CW BLUE Output Insulation class F WHITE GND Max. motor winding temp. 155 ºC EMC EN55014 IEC61000 Gear box Metal spur gears Motor pinion gear Plastic Metal Gear box material Zinc alloy Motor wiring Rod and house material Aluminum STKM11A Stroke length

Feedback Potentiometer RED Operating and storage temperature -26°C~+65°C Motor Manufacturing quality standards ISO 9001:2008 RoHS compliance Yes CE label Yes BLACK UL approval No Yes

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