MOBILE ROBOTS ADAPTIVE CONTROL USING NEURAL NETWORKS
I. Dumitrache, M. Dr ăgoicea
University “Politehnica” Bucharest Faculty of Control and Computers Automatic Control and System Engineering Department Splaiul Independentei 313, 77206 - Bucharest, Romania Tel.+40 1 4119918, Fax: +40 1 4119918 E-mail: {idumitrache, mdragoicea}@ics.pub.ro
Abstract: The paper proposes a feed-forward control strategy for mobile robot control that accounts for a non-linear model of the vehicle with interaction between inputs and outputs. It is possible to include specific model uncertainties in the dynamic model of the mobile robot in order to see how the control problem should be addressed taking into consideration the complete dynamic mobile robot model. By means of a neural network feed-forward controller a real non-linear mathematical model of the vehicle can be taken into consideration. The classical velocity control strategy can be extended using artificial neural networks in order to compensate for the modelling uncertainties. It is possible to develop an intelligent strategy for mobile robot control.
Keywords: intelligent control systems, mobile robots, autonomous navigation, artificial neural networks.
1. INTRODUCTION finding, representation of space, control architecture). The last function, control architecture, Technological improvements in the design and embodies all the other functions to allow the agent to development of the mechanics and electronics of the move in its environment. systems have been followed by the development of very efficient and elaborate control strategies. The Robot autonomy requests today the leading edge of framework of mobile robotics is challenging from advanced robotics research. The variety of tasks to both theoretical and experimental point of view. be performed by the robots from object manipulation to machine mobility, within a world environment The two important aspects related to mobile robotics which may be largely unknown and unpredictable can be addressed: a) the derivation of kinematic impose to take into consideration improved control and/or dynamic models for wheeled mobile robots, strategies for mobile robots. Based on the functional for particular prototypes as well as for general robots description of a robotic system (see figure 1), several equipped with wheels of several types; b) the mobile important issues are consequently brought up such as robot navigation problem that accounts for the the levels of modelling to be used, both for the task ability of the mobile vehicle to plan and execute and the work environment, the computational system collision-free motions in its environment. From an structure, the operating functionality and the sensor engineering point of view, the problem of navigation based execution control system. From an engineering can be addressed by taking into consideration a list point of view, the navigation problem (as a whole) of of functions (collision avoidance, localisation, path- a mobile robot can be accounted for based on the
following list of functions that defines elementary complex space structures with ever more demanding functionalities for navigating an autonomous mobile performance criteria. agent: representation of space, localisation, collision avoidance, path-finding, control architecture. 2. THE PROCESS Mobile vehicles are non-holonomic systems for which the control problem was addressed in A car-like mobile robot rolling on a flat ground was (Campion, et al ., 1991), (Bloch and Reyhanoglu, selected as a case study for the proposed control 1992), (d’Andrea Novel, et al ., 1995). Many other strategy. theoretical control problems have been studied concerning mobile vehicles, the difficulty of the This type of vehicle can be represented by a control problem depending also on the control rectangular shape moving in R 2 (figure 2). The objective, not only on the non-holonomic nature of movement of the robot in an empty space can be the system. Different architectures of autonomous described by the posture vector ξ = (x, y, θ), where control systems for mobile robots taking into (x, y) are the coordinates of the midpoint P between consideration intelligent techniques like fuzzy logic, the two rear wheels, and θ ∈ [0, 2 π) is the rotation neural networks, genetic algorithms and symbolic AI angle between the coordinate system that does not are presented in the literature (Tunstel et al. , 1998). move with the robot (x 0 O0 y0) and the coordinate system attached to the robot (x rPy r).
The linear velocity along the main axis of the robot • (V AV ) and its rotation velocity ( θ ) are the two parameters that determines the instantaneous motion of this type of vehicle. Based on these, the kinematic state model of the robot can be defined (Betourne, 1995):
• x1 = cos( x3 ) cos( x 4 ) u 1 • x2 = − sin( x3 ) cos( x 4 ) u 1 Figure 1 Functional description of a robotic system • 1 x 3 = sin(x ) u L 4 1 Even though significant progress has been made in (1) the study of such non-holonomic mechanical • x4 = u systems, both in the topic of modelling and control, 2 • there are still some problems to be addressed. One of 1 x 5 = u1 this refers to the control problem of non-holonomic r systems when the model of the system, in particular, • 1 x 6 =()cos(x ) + ( D / L ) sin( x ) u of the mobile vehicle, is affected by uncertainties, r 4 4 1 arising from neglected dynamics or parameter • 1 variations. In such cases, the performances of any x 7 =()cos(x4 ) − ( D / L ) sin( x 4 ) u 1 control strategy that uses such model will be r affected. This article proposes a control strategy 7 based on neural network architectures, that can take where the state vector is x = [x y θ φ ϕc ϕs ϕd ] ∈ R . into consideration this modelling uncertainties. With the above mentioned definitions, the equations Researches made in the recent years demonstrate that of the steering system can be rewritten: artificial neural networks (ANN) offer a great • promise for the modelling and control of non-linear x cos θ 0 systems. Even though the required network • η 1 (2) complexity for non-linear control applications and y= sinθ 0 = S ( q )η • η 2 the computational expenses are still important θ 0 1 problems to be solved, more and more results are reported in the field of neural control, such that ANN proved to be a real challenge for modern engineering technology that have to deal with increasingly
η V considered in the present paper combines the 1 AV stabilisation properties of an feedback conventional where =η = • , | η1| < VAv_max and | η2| η2 θ PID controller with the above mentioned learning • capabilities of a neural network based feed-forward < θ max . controller.
The entries of the vector η represent the velocity Conceptually, most of the approaches that accounts control inputs, and x 4 = φ is an internal state for neural networks based control structures make associated to the orientable wheel of the robot. use of the “inverse” model of the process as a controller. From this category, the two strategies that gained increased importance lately are IMC (Internal 3. NEURAL NETWORKS BASED Model Control) and feed-forward control. In this CONTROL STRATEGY article the feed-forward controller is implemented as a neural network controller that represents the The most important function necessary for inverse model of the process. navigating an autonomous agent, the control architecture, embodies all the other mentioned The mobile robot can be considered to be a two functions and makes the agent to be “alive”. In inputs - (the torques for the dc. motors) - two outputs particular, this work addresses a trajectory tracking (the linear velocity along the main axis, V AV , and the problem (Sarkar, 1994) in the presence of modelling • rotation velocity, θ ) system. uncertainties of the controlled system. An important control problem for mobile robots is to include The two levels hierarhical control structure is certain specific model uncertainties in the dynamic presented in figure 3. The inner loop is used to model of the mobile robot. It seems attractive to control the velocities of the wheels (velocity initiate an adaptive control for parameter control), while the outer loop forces the vehicle to uncertainties (e.g., unknown mass, wheel-radius; move on the desired trajectory (motion control). The etc…). motion controller is the generator of the velocities The aim of the present paper is to formulate a references for the velocity controller. control strategy for mobile robot control based on artificial neural networks (ANN). The approach
y Y r 0 ICR Y
ϕs ϕc φ D
D xr
θ ϕd
O0
L
X
X0
Figure 2 Posture definition
A feed-forward adaptive control strategy based on neural networks is used in order to implement the • a feedback component (PID control of linear and velocity controller. Figure 3 depicts the two • components of the velocity controller: angular velocities, V AV and θ ), based on a
simplified model of the process (dc motors and This component is important in improving the mobile platform) (equation 3) (Mazo, 1995); it system performances by learning on-line will stabilise the process and will reject the information about the process, through direct perturbations. interaction. Actually, this component will learn on-line the inverse dynamics of the process. •• 1 MV =()PP + AV2r d s In this way, it is possible to implement an adaptive •• r (3) control strategy at the execution level, based on J θ =()PP − 2D d s neural networks. The neural network (feed-forward controller) generates a command signal U that will k k k 60 N ff PN= M U −ME V − k I adjust the signal generated by the feedback controller, s,,, d R s d R 2πr s d M 0 a a Ufb , in order to minimise the velocity reference error, while compensating the modelling uncertainties. The where P l, r are the left/right torques obtained from original contribution of this work consists in the dc motors, M is the mass of the platform, r obtaining the command vector u = [U l Ur], using the radius of the wheels, D half distance between reference velocity vector ηc from the motion rear wheals, J the inertia momentum of the controller. The motion controller was implemented platform, N gear ratio, k M torque constant, R a following the procedure presented in (Kanayama, terminal rezistance, k E back emf constant, I 0 no 1990). load current, V l,r left/right wheels velocities. • a feed-forward component, with learning abilities, will allow a fast trajectory tracking.
Uff Feedforward Controller (NN)
Left motor Encoder η + Ul Gear box Feedback Controller (PID) Gear box Encoder
Ur Right motor Ufb
e q Motion p Controller Te ∫ S(q) ηc = f(e p, η, K) ηc = [V AV_c θ‘_c ] + qr
S(q)
ηr Figure 3 Two level hierarchical control structure
Some results are depicted in figures 4 and 5. Figure 4 presents results obtained using a feed-forward The typical evolution of the neural network outputs control strategy (average velocity, rotation velocity (the feed-forward control signal U ff ) is presented in and tracking errors). Figure 5 presents, for figure 6. comparison, the tracking errors for the two strategies (conventional PID and feed-forward with neural networks).
Figure 4 a) Figure 5 Tracking errors - conventional PID control versus neural networks feed-forward control
Figure 4 b) Figure 6 Neural network feed-forward controller outputs
4. CONCLUSIONS
This paper proposes a feed-forward control strategy for mobile robot control that accounts for the real non-linear model of the vehicle with interaction between inputs and outputs. In this respect, it is possible to include specific model uncertainties in the dynamic model of the mobile robot in order to see how the control problem should be addressed taking into consideration the complete dynamic mobile robot model. By means of a neural network feed-forward controller a real non-linear mathematical model of the vehicle can be taken into Figure 4 c)Velocity control - neural networks feed- consideration. The classical velocity control strategy forward control strategy was extended using artificial neural networks in order to compensate for the modelling uncertainties. In this way it is possible to develop an intelligent strategy for mobile robot control.
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