Autonomous Locomotion Mode Transition Simulation of a Track- legged Quadruped ’s Step Negotiation

Wang, J*; Ramirez-Serrano, A* & Davies, K. D.** * Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada ** Clearpath Inc., 97 Randall Dr, Waterloo, Ontario, N2V 1C5, Canada E-Mail: [email protected], aramirez@ucalgary, [email protected]

Abstract Multi-modal locomotion (e.g. terrestrial, aerial, and aquatic) is gaining increasing interest in robotics research as it improves the ’ environmental adaptability, locomotion versatility, and operational flexibility. Within the terrestrial multiple locomotion robots, the advantage of hybrid robots stems from their multiple (two or more) locomotion modes, among which robots can select from depending on the encountering terrain conditions. However, there are many challenges in improving the autonomy of the locomotion mode transition between their multiple locomotion modes. This work proposed a method to realize an autonomous locomotion mode transition of a track- legged quadruped robot’s steps negotiation. The autonomy of the decision-making process was realized by the proposed criterion to comparing energy performances of the rolling and locomotion modes. Two climbing gaits were proposed to achieve smooth steps negotiation behaviours for the energy evaluation purposes. Simulations showed autonomous locomotion mode transitions were realized for negotiations of steps with different height. The proposed method is generic enough to be utilized to other hybrid robots after some pre-studies of their locomotion’s energy performances.

Key Words: Hybrid Robots, Steps Negotiation, Energy Evaluation, Locomotion Mode Transition

1. INTRODUCTION Locomotion control of Unmanned Ground Vehicles (UGVs) through a heterogeneous environment is an ongoing challenge in mobile robotics research. To improve locomotion performance, or to gain high locomotion mobility, hybrid robots [1, 2] have been proposed to overcome uneven terrains by selecting the most appropriate locomotion [3] among designed multi-locomotion modes. The majority of proposed ground hybrid robots in the past two decades are wheel/track-legged systems due to their excellence in both locomotive efficiency and rough terrain negotiation abilities [4]. For these ground hybrid robots, two main locomotion modes can be categorized as rolling and walking. In general, there are two main technical complexities in the hybrid robotics research [3]: i) locomotion control to perform proper motions within each individual locomotion mode [5, 6] and ii) decision-making mechanism to select of the most appropriate locomotion among multi-locomotion modes depending on the current terrain properties [7, 8]. In the first problem, for wheel/track-legged robots, the rolling locomotion mode control problem is as same as the traditional wheeled/tracked robot that have received plenty of attention. For the walking locomotion mode of wheel/track-legged robots, although walking locomotion for traditional legged robots has been studied for decades, the locomotion research for hybrid robotics is still relatively limited [9]. For the second challenge, the development for decision-making mechanisms composed of locomotion mode transition criteria hasn’t been researched enough. In general, the locomotion mode transition of hybrid robots can either be realized by the “supervised autonomy” method [10], where switch decisions are made by human operators; or by autonomous locomotion

mode transition method, where robots switch their locomotion modes automatically based on pre-determined criteria. The supervised locomotion transition control requires continuous operator-robot interaction, which is not always available or reliable [11], especially when robots are used in a confined and complex environment for Urban Search and Rescue (USAR) tasks and other purposes where operators don’t have full situational awareness. One of the first researches related to the autonomous locomotion mode transition of ground hybrid robots is the development of a wheel-legged vehicle, Russian Moon Rover [12]. In their research, the challenge was to develop a locomotion module to switch between rolling and walking locomotion mode automatically. Three solutions with the different degree of , only mechanical mechanics, pre-programmed, and a feedback approach using onboard sensors’ information were proposed [8]. In the former two solutions, the locomotion switch is a pre-determined process with no decision-making module involved, while in the autonomous feedback solution, the vehicle executes the locomotion switch based on onboard sensors’ feedbacks that measure the terrain characteristics and the robot’s internal states. Since then, several solutions were proposed by combining particular mechanical mechanics designs [13] and pre-programmed solutions [5, 6, 14]. Although mechanical designs and pre-programmed solutions have improved the autonomy of the robot’s locomotion mode transition, the third autonomous solution is far behind and it’s still in the initial stage of development. In fact, the majority of hybrid robot locomotion transitions are realized by high-level control from operators. This’s true to the state-of-the-art wheel/track- legged robots including DRC-HUBO, CHIMP, Momaro, and RoboSimian, four of the five top teams’ robot designs developed for the 2015 DARPA Robotics Challenge [15]. One of the significant challenges to realize the autonomous locomotion transition is the requirement of an effective sensing method to evaluate the vehicle-terrain interaction characteristics (known as terramechanics) and terrain parameters reliably and efficiently. The terramechanics methods for modelling vehicle-terrain interactions are based on the identification of soil properties, which requires significant in-place measurements of soil characteristics prior to the robot being deployed [8]. Moreover, the terramechanics model methods that try to predict the robot-terrain interaction are heavily computational expensive [16]. So terramechanics methods are inadequate to be used for the autonomous locomotion mode transition directly, especially when robots are required to operate at high speed such as in USAR operations. An alternative solution to terra-mechanics methods measuring vehicle- terrain interactions directly, energy consumption was used as a criterion to evaluate the transverse-ability of each individual locomotion mode of wheel/track-legged robots [8, 17]. Other generic parameters, including stability margin [7] and motion efficiency [3] were also studied trying to realize the autonomous locomotion transition. Within the reviewed literature, Gorilla [3, 7] realized autonomous locomotion mode transitions between biped walking and quadruped walking using criterion developed with stability margin and motion efficiency; WorkPartner [8] showed the ability to switch locomotion modes between rolling and rolking (rolling and walking simultaneously) automatically depending on criteria derived with energy consumption, slip percentage of wheels, and resistance forces of wheel-terrain. However, Gorilla is a with walking locomotion only rather than a wheel/track-legged hybrid robot; the proposed method of WorkPartner works particularly to the WorkPartner robot platform. Moreover, threshold values of the proposed locomotion transition criteria for WorkPartner were “set to” empirical numbers based on prior experiment tests on the targeted terrains. More importantly, the existing proposed criteria for locomotion mode transition were developed with internal states of the robot only without considering the external environmental information, which may cause serious troubles such as local minima [18].

In this study, a novel autonomous locomotion mode transition method was proposed based on the criterion derived with both the internal state of robots, i.e. energy consumption, and the external environmental information, i.e. geometrical heights of encountering steps. The threshold values of the locomotion mode transition criterion were determined by energy evaluations of the walking locomotion mode performance. In order to evaluate the energy performance for quadrupedal wheel/track-legged hybrid robots to negotiate steps in the walking locomotion mode, two climbing gaits were proposed to realize proper locomotion behaviours. The proposed method to realize an autonomous locomotion mode transitions for step negotiation purposes doesn’t depend on specific mechanical designs, thus is applicable to different quadrupedal wheel/track-legged hybrid robots. The paper is organized as follows: section 2 explained the rolling and walking locomotion modes of the hybrid robot and two steps negotiation gaits for quadrupedal wheel/track-legged hybrid robots developed based on the Cricket system. Section 3 showed the mathematical equations used for the energy calculations. Section 4 presented the proposed autonomous locomotion transition method and simulation results. Section V concluded the paper and discussed the future work.

2. SIMULATION MODEL DEVELOPMENT This work focuses on the locomotion mode transition between two main locomotion modes of wheel/track-legged hybrid robots: rolling and walking. Rolling indicates that all tracks/wheels are used for the vehicle propulsion with all articulated legs fixed to a particular configuration. Walking includes all sub-locomotion modes that involve the movement of articulated legs. Thus, walking on flat terrains, and climbing negotiation of rough terrains are both categorized as the walking locomotion mode. Due to the fact that rolling locomotion is both time and energy efficient on flat hard terrains without irregularities and discontinuities, the default and primary locomotion mode for the majority of hybrid ground robots are rolling [19]. The locomotion mode may need to switch from rolling to walking when negotiating rough terrains such as steps. Because the rolling locomotion mode of the wheel/track-legged hybrid robots is as same as the rolling locomotion of the traditional wheeled/tracked robots, the walking locomotion mode control is one of the research focuses in this study. 2.1 The Cricket Robot Platform The hybrid robot employed in this study, Cricket [20] was designed as a fully autonomous track-legged quadruped robot. The robot’s locomotion system resembles as a quadrupedal hybrid robot with four revolute joints on each leg shown in Fig.1. In addition to four revolute joints, each leg features a drivable track encircling the outermost leg segment, which allows the robot to drive in a similar fashion to conventional skid-steer tank robots. Furthermore, the Cricket robot is capable to perform sophisticated manoeuvres not possible by traditional tracked vehicles such as rough terrain negotiations in its walking locomotion mode [21]. The track designs in the current robot prototype can also be replaced with wheels or any other feet configurations if desired. The locomotion system of the Cricket robot enables two main forms of movement: rolling using tracks or wheels for efficient travel on open semi-flat terrains and walking for traversing complex rough terrain. These two locomotion modes are referred as rolling and walking within the context of this study.

Figure 1: The prototype of the Cricket and its leg joints layout in SolidWorks [21]. 2.2 Rolling Locomotion Mode of the Cricket As same as the majority of wheel/track-legged hybrid robots, the default locomotion mode of the Cricket robot is rolling due to its time and energy efficient on flat hard terrains. In the rolling locomotion mode, the robot was fixed to be the home configuration where all joints are at their centre positions as shown in Fig. 2.

Figure 2: The home configuration and leg joints’ positions of the Cricket robot in V-REP [22]. 2.3 Walking Locomotion Mode of the Cricket For the steps negotiation applications, proper climbing gaits are needed to achieve smooth walking performances. The walking gait design includes body adjustments and leg movements, both of which involve inverse kinematics calculations. The kinematics calculations were derived by attaching coordinate frames to each link of all legs and the body following the traditional Denavit-Hartenberg (D-H) method [23] as shown in Fig. 3. The D-H parameters of the front left leg were listed in Tab. I. Parameters of the other three legs are similar (with sign differences only) due to the symmetrical mechanical design of the Cricket.

Table I: D-H parameters of the front left leg.

Link 𝒃𝒊 𝜽𝒊 𝒂𝒊 𝜶𝒊 1 0 𝜃 0 𝜋/2 2 𝑏 0.1020 𝜃 𝑎 0.1330 0 3 𝑏 0.0185 𝜃 𝑎 0.1850 0 4 𝑏 0.0285 𝜃 𝑎 0.2196 0

The homogeneous transformation matrix between the Cricket’s track tip (Frame 5) and the shoulder frame (Frame 1) shown in Fig. 3 was calculated as: 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑐𝑐 𝑐𝑠 𝑠 𝑏 𝑏 𝑏𝑠 𝑐𝑎𝑐 𝑎𝑐 𝑎𝑐 𝑠 𝑐 𝑠 𝑠 𝑐 𝑏 𝑏 𝑏 𝑐 𝑠 𝑎 𝑐 𝑎 𝑐 𝑎 𝑐 (1) 𝑠 𝑐 0𝑎𝑠 𝑎𝑠 𝑎𝑠 000 1 where 𝑠 and 𝑐 represents sin 𝜃 and cos 𝜃 , respectively; 𝑠 and 𝑐 represents sin𝜃 𝜃 and cos𝜃 𝜃, respectively; and 𝑠 and 𝑐 represents sin𝜃 𝜃 𝜃 and cos𝜃 𝜃 𝜃, respectively.

Figure 3: Frames assignment of the front left leg links and V-REP simulation model. The climbing gaits were then created by the position control of the track tips. A fifth-order polynomial and its’ first and second derivatives [24], satisfying six constraints, i.e. position, velocity, and acceleration at the initial and final states, were derived to define smooth trajectories of each joint. The inverse kinematics calculation was conducted using the Reflexxes Motion Library IV [25]. Although legged locomotion gaits have been studied for decades, researches of the locomotion of wheel-legged robots are much more recent [9]. The step climbing gait of ground hybrid robots with complex mechanical designs (articulated leg with more than three degree-of-freedom) research is especially limited. The proposed two climbing gaits were the whole body climbing and the rear body climbing to negotiate steps height of ℎ, 2ℎ and 3ℎ (ℎ indicates the track height shown in Fig. 3) shown in Fig. 4 and Fig. 5, respectively. The whole body climbing gait means both front and rear legs negotiate steps by the walking locomotion, the rear body climbing gait indicates that front legs negotiate steps by the rolling locomotion and rear legs using the walking locomotion. In the whole body climbing gait, the body of the robot was moved forward and backward first in order to gain more stability margins before the legs’ gradually forward movements. More details about the whole body climbing gait can refer to [26]. In the rear body climbing gait, rears legs were lifted up to the negotiating steps when the front legs and body had already moved up on the step by the rolling locomotion.

The reason for proposing the rear body climbing gait is due to the fact that it’s always the rear wheels limit the steps negotiation mobility of the rolling locomotion for the quadruped wheel/track-legged hybrid robots, the rear body climbing gait is a good complementary steps negotiation strategy for the whole body climbing gait.

Figure 4: The whole body climbing gait of steps negotiation in V-REP [22].

Figure 5: The rear body climbing gait of step negotiation in V-REP [22].

3. ENERGY CONSUMPTION CALCULATIONS In order to handle the robot dynamics and evaluate the energy consumption of steps negotiation accurately and effectively, a built-in physical engine of a robotics simulation software V-REP [27], Vortex was used. The studied dynamics modelling method of the generic rolling and climbing locomotion mode and energy criterion verification of Cricket’s step negotiation was conducted in [28]. For a DC motor, the energy consumed during a time 𝑇can be evaluated by [24]: 𝐸 𝑈𝐼 𝑑𝑡 𝜏𝜃 𝑑𝑡 𝐼 𝑅 𝑑𝑡 (2)

Where 𝑈 and 𝐼 is the applied voltage and armature current respectively, 𝜏 indicates the joint torque, 𝜃 represents the joint angular velocity, and 𝑅 is the armature resistance.

The joint torque τ can be derived as:

𝜏𝐾𝐼 (3) where 𝐾 denotes the torque constant. In Eq. (2), the first term is the mechanical energy and the second part calculates the energy loss due to heat emissions. Although a negative value for the first term, i.e. mechanical energy indicates a gain in energy supplied by external forces, DC motors can’t store this energy [24]. Therefore, the energy consumed by the DC motors during a time 𝑇 can be calculated as: 𝐸 𝑓𝜏𝜃 𝑑𝑡 𝐼 𝑅 𝑑𝑡 (4) 𝜏𝜃 when 𝜏𝜃 0 where 𝑓𝜏𝜃 . 0when 𝜏𝜃 0 In this study, the energy consumption of steps negotiation can be evaluated by combing Eq. (3) and (4) as: 𝜏 𝐸 𝐸 𝑓𝜏 𝜃 𝑅 𝑑𝑡 (5) 𝐾

Where 𝑇 is the negotiation time, 𝐸 represents energy consumption of the actuated joint 𝑖, 𝑛is the number of actuated joints, and 𝑑𝑡 represents the time step.

4. LOCOMOTION MODE TRANSITION SIMULATIONS This section presents simulation results of Cricket’s step negotiation performance using the autonomous locomotion mode transition method. First the autonomous locomotion mode transition method is proposed, next the simulation settings are specified, then the energy performance of the step climbing gaits proposed in section 2 are evaluated in order to determine the criterion threshold values, last case studies of the steps negotiation with ℎ, 2ℎ, and 3ℎ heights are shown to verify the proposed method. 4.1 Autonomous Locomotion Mode Transition Method The autonomous locomotion mode transition method works in the following manner shown in Fig. 6. The robot starts to negotiate steps by the rolling locomotion, measuring and recording the energy consumption since the negotiation starts (𝐸); at the same time, comparing to the pre-studied energy consumption of the walking locomotion mode (𝐸 ); determining the threshold values (𝑇) by the energy consumption 𝐸 (𝑇 is defined as same as 𝐸); executing a decision-making process in a way that if 𝐸 𝐸 , the robot switches from rolling to walking locomotion until one climbing gait cycle finishes, then switches back to rolling locomotion; otherwise if 𝐸 𝐸, the robot keeps rolling. The on-line measuring and recording of the rolling energy evaluations include the energy consumption of the whole step negotiation (𝐸) and the rear body negotiation (𝐸). The pre-studied climbing energy consumption 𝐸 also contains both the whole body climbing energy (𝐸) and rear body climbing energy (𝐸). Thus, the locomotion transition can be invoked by either 𝐸 𝑇 or 𝐸 𝑇 in the decision-making process.

Figure 6. Flowchart of the autonomous locomotion mode transition for steps negotiation. 4.2 Simulation Settings The overall hierarchical scheme of the autonomous locomotion mode transition control was shown in Fig. 7. The outside loop conducted the decision-making process of the locomotion mode transition in MATLAB, and the inner loop controlled each individual locomotion mode in V-REP. A link between the MATLAB environment and the robot’s physical model (built in V-REP) was established using the remote API functionality of the V-REP simulation environment.

Figure 7. Overall hierarchical scheme of the autonomous locomotion mode transition control. In V-REP, the rolling locomotion was controlled to maintain the home configuration and the desired vehicle velocity. The walking locomotion control was realized by using the climbing gaits generated based on the step height information explained in section 2. The kinematics and dynamics calculations of the motion control for both the rolling locomotion and the walking locomotion were handled in V-REP. The simulation results including the joint torque and the joint angular velocity were sent to MATLAB to conduct data analysis and energy consumption calculations. The simulations were conducted with a 2-millisecond time step to approximate real-time dynamics of the step negotiation.

4.3 Walking Locomotion Energy Evaluation In the step negotiation simulations, it had been observed that the rolling locomotion can’t transverse over steps with height more than 3ℎ due to the track traction forces limitation. It’s obvious that the locomotion mode transition can only happen when the steps negotiation can be achieved by both the rolling and climbing locomotion modes. Thus, the energy evaluations of the step negotiation with heights of ℎ, 2ℎ and 3ℎ using the whole body climbing and the rear body climbing gaits were conducted. The overall energy consumption performance of the two locomotion modes was evaluated first by conducting the power evaluations. Because the rear body climbing can be considered as the rear portion of the whole body climbing gait, only the power consumption of the whole body climbing gait was presented in Fig. 8. By showing the overall energy consumption intensity, it’s a straightforward approach to compare the two locomotion with different step negotiation time. Within the walking gait, the joint accelerations were held constant between tests leading to differences in the time required to overcome obstacles of differing heights – higher obstacles took longer to step over. As the time required to overcome a step also varied in the case of rolling locomotion, the simulation time and power consumption in Fig. 8 were presented in a normalized form with respect to the total negotiation time. The plots from top to bottom represent the power consumption for the robot overcomes steps with heights of ℎ, 2ℎ and 3ℎ respectively.

Figure 8. Step Negotiation Power Comparison of the Rolling and Climbing Locomotion. For both rolling and walking locomotion modes, the energy consumption was evaluated from the position the vehicle starts to negotiate the step to the whole robot finished the steps negotiation. The energy consumption of the whole body climbing and rear body climbing with step heights of ℎ, 2ℎ and 3ℎ were evaluated shown in Fig. 9 and Fig. 10. It could be noticed that the differences of the energy consumption using the whole body climbing gait with different step heights were small in Fig. 9. This was due to the fact that the climbing gaits were defined to have the same desired joint accelerations, the leg stride length, and the forward movement height [22]. Thus, the differences of the energy consumption of the different step negotiations only came from the negotiation time and the body adjustment. The

energy consumption of the rear body climbing with step heights of ℎ, 2ℎ and 3ℎ were evaluated shown in Fig. 10.

Figure 9. Accumulated energy consumption using the whole body climbing gait.

Figure 10. Accumulated energy consumption using the rear body climbing gait.

As shown in Fig. 6, the threshold values of the energy criterion (𝑇 and 𝑇 ) were determined by the pre-studied energy evaluations of the walking locomotion to negotiate steps with different heights using the whole body climbing and the rear body climbing gates. In this study, the threshold values were defined to be equal to the energy consumption of the walking locomotion using the whole body climbing and the rear body climbing gaits, thus the threshold values were obtained by the energy evaluation results shown in Fig. 9 and Fig. 10. It can be concluded that the threshold values were not based on empirical values like in other methods [3, 8], instead a novel rule based on the evaluation of the alternative locomotion mode was used to determine the threshold values. Moreover, the threshold values

weren’t fixed, they were determined by the robot’s negotiation terrain profiles. As shown in Fig. 9 and Fig. 10, the energy evaluation case studies for the whole body climbing and the rear body climbing gaits to negotiate step heights of ℎ , 2ℎ and 3ℎ were evaluated respectively. 4.4 Simulation Results The steps negotiation simulations with heights of ℎ, 2ℎ and 3ℎ were conducted as case studies to verify the proposed autonomous locomotion mode transition method. In the simulations, the energy consumption of the whole body negotiation (𝐸) and the rear track negotiation (𝐸) are recorded on-line to compare to pre-studied the whole body climbing energy evaluation results (𝐸) shown in Fig. 9 and the rear body climbing energy evaluation results (𝐸) shown in Fig. 10, respectively. The energy consumption of the step negotiation in rolling locomotion mode only (without utilizing the proposed locomotion mode transition method) was plotted together with the on-line energy recordings. Thus, the energy advantage by using the proposed method can be seen in the Fig. 11, 12 and 13. In Fig. 11, both 𝐸 𝐸 and 𝐸 𝐸 were satisfied for the whole step negotiation process, so the robot finished negotiating the step with ℎ height in the rolling locomotion mode without conducting the locomotion mode transition.

Figure 11. Energy consumption simulation of the step negotiation with ℎ height.

In Fig. 12, it showed that when the robot negotiated a step with 2ℎ height, the locomotion mode transition was invoked. The robot changed from the rolling to walking locomotion mode when 𝐸 𝐸 was satisfied. Between rolling and walking locomotion mode, there was a defined locomotion transition preparation phase, during which the robot moved backward for a small distance to make sure that the rear track got apart from the steps. When the robot negotiated step with 3ℎ height shown in Fig. 13, the locomotion mode transition also got involved when the rear body energy consumption using rolling locomotion mode passed over the threshold value shown in Fig. 10. It can be seen that it was much more energy efficient to conduct the steps negotiation using the proposed autonomous locomotion

mode transition method compared to the step negotiations using the rolling locomotion mode only.

Figure 12. Energy consumption simulation of the step negotiation with 2ℎ height.

Figure 13. Energy consumption simulation of the step negotiation with 3ℎ height. In this section, an energy criterion method was proposed and successfully realized the autonomous locomotion mode transitions of the Cricket robot when it negotiated steps with

different heights. Compared with pure rolling negotiation, the energy performances were improved significantly, this was especially true to the steps with big height. One of the most important parameters, the transition criterion threshold values were determined by the alternative locomotion mode studies rather than empirical settings.

5. CONCLUSION This study realized an autonomous locomotion mode transition of a track-legged quadruped robot’s steps negotiation by proposing a energy criterion-based method. The proposed locomotion mode transition method is generic enough to be applied to different hybrid robots. When applying the method to a new hybrid robot, the threshold values should be determined first by conducting the energy evaluations of the robot's walking locomotion mode. In this study, three case studies of the steps negotiation simulations were conducted, more energy evaluations of the walking locomotion to negotiate different step heights can be pre- evaluated and interpolated as a look-up table. Moreover, even though it is a commonly used steps negotiation strategy for wheel/track-legged robots [28, 29], the proposed climbing gaits haven’t been verified to be energy optimal. Future work can be conducted to optimize the climbing gait with respect to the energy consumption.

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