Design of a Compliant Bipedal Walking Controller for the DARPA Robotics Challenge

Transcription

1 Design of a Compliant Bipedal Walking Controller for the DARPA Robotics Challenge Michael A. Hopkins, Robert J. Griffin, Alexander Leonessa *, Brian Y. Lattimer and Tomonari Furukawa Abstract This paper provides an overview of the bipedal walking controller implemented on ESCHER, a new torquecontrolled humanoid designed by Virginia Tech to compete in the DARPA Robotics Challenge (DRC). The robot s compliant control approach relies on an optimization-based inverse dynamics solver proposed in a previous publication. This work presents two unique features to improve stability on soft and uncertain terrain, developed in preparation for the dirt track and stairs task at the DRC Finals. First, a step adjustment algorithm is introduced to modify the swing foot position based on the divergent component of motion (DCM) error. Second, a simple heuristic is introduced to improve stability on compliant surfaces such as dirt and grass by modifying the design of the center of pressure (CoP) trajectory. The proposed approach is validated through DRC-related experiments demonstrating the robot s ability to climb stairs and traverse soft terrain. I. INTRODUCTION As bipeds, humanoid robots have the potential to achieve excellent mobility in natural and man-made environments, ideally matching the robustness and versatility of humans. The DARPA Robotic Challenge (DRC) helped bring a new generation of bipedal walking controllers to real hardware systems. Nevertheless, the high risk of failure at the competition indicates that a number of challenges still remain before bipeds can reliably negotiate difficult real-world scenarios. In [1], the authors presented an optimization-based wholebody controller enabling the THOR humanoid to walk on flat terrain using series elastic actuation. In preparation for the DRC, this approach was ported to ESCHER, a new 1.8 m tall humanoid developed at Virginia Tech (see Fig. 1). This paper provides an overview of the final bipedal walking controller used at competition, including a discussion of design considerations related to the dirt track and stairs task. The presented controls approach is an iteration of a previously published design which relies on divergent component of motion (DCM) tracking to stabilize the centroidal dynamics [1 3]. Two unique features are introduced to improve stability on soft and uncertain terrain. First, a new step adjustment algorithm is proposed to modify the swing foot trajectory during the single support phase using a simple heuristic based on the instantaneous DCM tracking error. Second, a simple, yet surprisingly effective modification to the nominal center of pressure (CoP) trajectory is introduced to reduce tracking errors on soft terrain. The proposed approach is verified through a variety of walking and push recovery experiments conducted using the ESCHER humanoid. The authors are with the Terrestrial Robotics, Engineering & Controls Laboratory (TREC) at Virginia Tech. ( robert.griffin@vt.edu) * This material is based upon work supported by (while serving at) the National Science Foundation. Fig. 1. Left: THOR humanoid walking on the Ex-USS Shadwell as part of the ONR Shipboard Autonomous Firefighting Robot (SAFFiR) program (photo courtesy of Virginia Tech / Logan Thomas). Right: ESCHER humanoid walking on the dirt track at the DARPA Robotics Challenge Finals (photo courtesy of DARPA). II. RELATED WORK A number of top-performing DRC teams developed compliant whole-body control strategies to enable the Atlas humanoid, supplied by Boston Dynamics, to traverse the final course [4 6]. As in [7 10], these approaches compute admissible joint torque and acceleration setpoints for whole-body control by solving an efficient convex optimization based on the rigid body dynamics. Feng et al. developed a hybrid inverse dynamics and inverse kinematics solver to enable the Atlas robot to walk on uneven terrain [4]. Kuindersma et al. stabilized the walking gait by minimizing an LQR cost function based on the zero moment point (ZMP) [5]. Johnson et al. and Koolen et al. tracked an instantaneous capture point (ICP) trajectory using an approach similar to the DCM-based controller presented in this paper [6, 11]. While several authors have proposed methods to improve walking on soft terrain including grass and sand [12, 13], experimental results are limited. Online adjustment of the target foothold position is a well-known approach to increase stability in response to external disturbances and unmodeled terrain features. A number of publications have presented reactive stepping strategies based on the linear inverted pendulum dynamics [14 16]. Englsberger et al. proposed a method to determine the upcoming foothold position given the desired DCM position at the end of the next step [17]. Unlike the method presented here, the authors computed the step adjustment based on the extrapolated DCM position at the time of heel-strike.

2 A. Hardware Design III. DESIGN AND MODELING In preparation for the 2013 DRC Trials, Virginia Tech developed the THOR humanoid, a 63 kg prototype platform featuring a compliant lower body with human-like range of motion [18]. The increased autonomy and run-time requirements of the DRC Finals spurred a design iteration leading to the development of ESCHER, the Electric Series Compliant Humanoid for Emergency Response. At 77 kg, the revised design features a new upper body with 11 DoF manipulators from HDT Global and onboard power and computing for extended operation. The hip pitch and knee assemblies were also upgraded to achieve the necessary output torque for locomotion on uneven terrain. Like its predecessor, ESCHER features custom linear series elastic actuators, enabling compliant control of all 12 degrees of freedom (DoF) in the lower body [19]. A titanium leaf spring is mounted in series with the actuator load to increase shock tolerance and decrease mechanical impedance. In-line load cell sensors provide direct force measurements to enable high-performance torque and impedance control of the hip, knee, and ankle joints. B. Dynamic Models As in [4 6], the presented controls approach employs a rigid body model to approximate the whole-body dynamics of an articulated humanoid. Assuming each joint behaves like an ideal torque source, the floating-base rigid body equations of motion are given by [ ] 0 = H q + C J T c f c, (1) τ where τ R n is the vector of joint torques, q R n+6 is the vector of generalized coordinates, and f c R 3 is the vector of external forces acting at each contact point, c = 1... N, with corresponding Jacobian, J c. Here H and C represent the joint-space inertia matrix and vector of centrifugal, Coriolis, and gravity torques, respectively. As in [9], approximate no-slip conditions are expressed by constraining the acceleration of each contact point using the equality, J c q + J c q = 0. The controls approach presented in Section IV makes extensive use of the divergent component of motion (DCM) to stabilize the centroidal dynamics of the rigid body system during walking. The DCM represents a linear transformation of the CoM state that partitions the second-order linear inverted pendulum dynamics into coupled first-order systems [17, 20]. Appropriate planning of the DCM can be used to ensure that the CoM is stabilizable following one or more steps. Assuming a constant CoM height, the closely related ICP defines the two-dimensional point at which the centroidal moment pivot (CMP) must be placed for the CoM to come to a complete rest [14], whereas the DCM defines the three-dimensional point at which the CoM converges. Using the time-varying formulation presented in [2], the DCM is defined as ξ = x + 1 ẋ, (2) ω Fig. 2. Left: DCM dynamics and external forces acting on an articulated humanoid. Right: Lateral step adjustment based on the estimated DCM error. Here r foot,r and r foot,r are the nominal and adjusted swing foot positions. where x R 3 is the CoM position and ω(t) > 0 is the timevarying natural frequency of the transformed CoM dynamics, ẋ = ω (ξ x). The coupled first-order DCM dynamics are given by ( ξ = ω ω ) (ξ r vrp ), (3) ω where r vrp R 3 represents the virtual repellent point (VRP) [2, 17]. Given (ω ω/ω) > 0, the VRP repels the DCM at a rate proportional to its distance; by definition, this threedimensional point maps the position of the CoM to the total linear momentum rate of change acting on the system, l = m(ω 2 ω)(x r vrp ). (4) Note that the linear momentum rate of change is related to the net contact force via Newton s second law, i.e. l = mẍ = f c + f g, where f g = [ 0, 0, mg ] T is the force of gravity and m is the total mass of the robot. The various reference points related to the DCM dynamics are illustrated in Fig. 2, including the enhanced centroidal moment pivot (ecmp) which maps the CoM position to the net contact force, f c = m(ω 2 ω)(x r ecmp ) [2, 17]. The ecmp is typically collocated with the center of pressure (CoP) in the robot s base of support to ensure that the line of action passes through the CoM. This results in a net horizontal angular momentum rate of change of zero. Note that the VRP lies directly above the ecmp with a vertical offset of z vrp = g/(ω 2 ω), determined by the gravitational constant and natural frequency [2]. Thus, if ω = 0, the natural frequency is given by ω = g IV. CONTROLS APPROACH z vrp. Figure 3 includes a high-level block diagram of the bipedal walking controller developed for the ESCHER humanoid. The presented controls approach is an extension of the compliant locomotion framework described in [1]. This section provides a summary of the overall design including a new step adjustment algorithm based on the DCM dynamics.

3 Fig. 3. High-level block diagram of ESCHER s stepping controller. Note that some control paths have been omitted to improve readability. A. State Machine Single-step and multi-step behaviors are implemented using the finite state machine depicted on the far left of Fig. 3 which transitions between various contact phases including double support, toe-off, single support, and heel-strike. In double support, both feet are assumed to be in contact with the surface. If an ankle or knee pitch limit is encountered by the predefined swing foot prior to single support, the robot transitions to a reactive toe-off state to compensate for the leg range of motion limits. Once the heel is unloaded, the swing foot rotates about the toe contact points, shifting the ankle pitch away from the soft limit. During single support, the swing foot travels to a new foothold position. After a predetermined duration, the state machine transitions to heelstrike, at which point the swing foot is lowered at a constant velocity until it contacts the ground and settles into a new foothold pose. When the foot is sufficiently loaded, the state machine transitions back to double support. B. Task-Space Planning The step controller obtains desired foothold poses and step durations from a footstep queue that is continuously populated by a high-level planner. As illustrated in Fig. 3, several mid-level planners are defined to compute task-space reference trajectories for the swing foot, pelvis, and DCM at the beginning of each double support phase. The DCM reference trajectory is generated using the realtime numeric planner described in [2]. First, a nominal CoP and ecmp trajectory is computed from the desired foothold poses to ensure no-tip conditions during each support phase. Second, the time-varying natural frequency, ω(t), is derived from the desired vertical CoM and ecmp trajectories. Third, an initial DCM reference trajectory is generated via reversetime integration of the DCM dynamics (3). Finally, the planner solves a time-varying LQR optimization to refine the trajectory over a short preview window, thereby eliminating any initial discontinuities due to replanning. Although more computationally intensive than the analytical DCM planners proposed by Englsberger et al. [17, 21], the proposed approach permits generic CoP and vertical CoM trajectories. The pelvis rotation and swing foot pose, R pelvis,r (t), R foot,r (t), and r foot,r (t), are generated using piecewise minimum jerk trajectories that interpolate between intermediate waypoints determined from the initial and final foothold poses. The upper body joint trajectories, q r (t), are defined by an internal planner that manages arm swinging during stepping. During manipulation, these trajectories are determined by an external planner that manages end-effector positioning and collision avoidance for tasks such as grasping and carrying an object. C. Task-Space Control Task-space position and velocity errors are regulated using a set of feedback controllers that command desired taskspace forces and accelerations. Table I lists the proportional and derivative gains used to compute desired linear and angular momentum rates of change, pelvis and swing foot accelerations, and upper body joint accelerations for the experiments in Section VI. To maintain rotation invariance, x and y-axis gains are represented in pelvis yaw coordinates. The computed motion tasks are tracked using the quadratic program (QP) formulation described in Section IV-E. The desired linear momentum rate of change is derived using a DCM tracking controller designed to stabilize the centroidal dynamics. This VRP-based controller uses PI feedback to regulate the estimated DCM error as described in [2]. The VRP setpoint is mapped to a desired linear momentum rate of change, l d, using (4). Proportional and integral gains of 3 m/m and 1 m/m s were selected for the experiments presented in Section VI, noting that the integral action is disabled during single support and heel-strike. The desired angular momentum rate of change is given by k d = 0. This reflects the assumption that the ecmp and CoP are collocated during walking, in which case, the horizontal moment about the CoM is equal to zero. Note that the robot s angular momentum is not directly regulated using feedback control. The proposed approach relies on Cartesian and joint-space PID controllers to track the pelvis, swing foot, and upper body trajectories and prevent excessive angular momentum during walking.

4 D. Step Adjustment In the event of a disturbance, the momentum controller will attempt to stabilize the DCM by shifting the ecmp and CoP away from the nominal reference position. This can induce a significant moment about the CoM whenever the ecmp leaves the base of support. Due to the robot s limited range of motion, it is not always possible to sustain the corresponding angular momentum rates of change required to prevent a fall, especially during the single support phase. In such scenarios, a fall can often be avoided by adjusting the target foothold position to modify the base of support. The proposed controller employs a simple heuristic to implement real-time step adjustment in response to significant disturbances. As illustrated in Fig. 3, a feedforward path is included to adjust the nominal swing foot trajectory in response to the DCM tracking error. The reference position is given by r foot,r = projection ( r foot,r + deadband (ξ ξ r ) ), (5) where r foot,r is the nominal swing foot position, ξ is the estimated DCM position, and ξ r is the reference DCM position. The deadband function implements a neutral zone in the DCM error signal to maintain precise foothold tracking in the event of small disturbances. The vertical DCM error is eliminated to avoid early or late heel-strike events. The projection function projects the modified swing foot position into a safe region based on a conservative estimate of the collision-free state space. Figure 2 illustrates an ideal lateral step adjustment in response to a large DCM error. Note that the offset between the final DCM and swing foot position is equivalent to the offset between the reference DCM and swing foot position (assuming zero deadband). The future foothold positions are specified relative to the current support foot position. Thus, the responsibility to correct for horizontal drift in foothold tracking is tasked to the high-level footstep planner. In scenarios requiring precise foothold tracking, the step adjustment can be minimized by increasing the DCM error deadband or increasing the DCM controller stiffness. E. Inverse Dynamics (QP Formulation) Given desired task-space forces and accelerations at each time step, an inverse dynamics module is used to compute optimal joint accelerations, q, and generalized contact forces, ρ = [ ] ρ T 1... ρ T T N, by minimizing a quadratic cost function in the form, min q,ρ C b (b J 2 q J q) + λ q q 2 + λ ρ ρ 2. (6) Here b represents the vector of desired motion tasks, J represents the corresponding matrix of task-space Jacobians, Q b = C T b C b represents the task weighting matrix, and λ q and λ ρ define the regularization parameters. The QP includes linear Newton-Euler and Coulomb friction constraints in addition to joint position and torque limits to ensure dynamic feasibility of the optimized setpoints [1]. Table I lists the experimentally selected weights for each motion task. TABLE I WHOLE-BODY CONTROLLER WEIGHTS AND GAINS 1 Motion Task Units Weight P-Gain D-Gain l d N 5, 5, k d Nm 5, 5, ω pelvis,d rad/s 2 100, 100, , 70, 30 30, 30, 15 ω foot,d rad/s 2 500, 500, , 100, 75 5, 5, 5 r foot,d m/s 2 1e3, 1e3, 1e3 50, 50, , 35, 35 r contact,d m/s 2 1e5, 1e5, 1e5 0, 0, 0 0, 0, 0 q arm,d rad/s q waist,d rad/s F. Low-Level Control Joint torque setpoints are derived from the optimized joint accelerations and contact forces via the rigid body equations of motion (1). As illustrated in Fig. 3, joint velocity setpoints are obtained via leaky integration of the optimized joint accelerations. The computed torque and velocity setpoints are relayed to embedded motor controllers at a rate of 150 Hz. The update rate is currently limited by the robot s state estimator, which computes velocity estimates using a decoupled Kalman filter design. Upper body trajectories are tracked using a high-gain velocity controller for each DoF, while lower body trajectories are tracked using a low-gain impedance controller described in [3]. V. DESIGN CONSIDERATIONS FOR THE DRC This section presents implementation details and lessons learned in adapting ESCHER s walking controller to two of the challenges presented by the DRC Finals: the dirt track and the stairs task. A. Dirt Track As ESCHER was unable to attempt the driving task at the DRC, the robot was required to traverse the 200 ft dirt track on foot. Because the QP formulation presented in Section IV-E assumes a rigid contact model, soft terrain, such as dirt and grass, can introduce significant unmodeled dynamics during walking. Although low-impedance control of the lower body provides a certain degree of robustness to surface compliance, poor DCM tracking can lead to tipping as the CoP deviates to the edge of the support polygon. In particular, lateral tipping about the outside edge of the foot can occur when the momentum controller fails to prevent overshoot of the DCM trajectory near the end of the double support phase. This failure mode is particularly dangerous, as range of motion and self-collision risks often prevent proper step adjustment during single support. During the course of development, the authors found that a simple modification to the CoP reference trajectory could significantly improve performance on soft and uncertain terrain. In the bipedal walking literature, the CoP trajectory is often defined to pass through the center of each support foot. A notable exception is [22], where the authors shift the 1 Cartesian weights and gains are specified for the x, y, and z axes. 2 These weights are decreased to (2.5, 5, 1) during the single support phase to reduce oscillations in the sagittal plane.

5 Fig. 4. The nominal CoP trajectory is shifted towards the inside of the support foot to improve stability on soft terrain and reduce lateral motion of the CoM during walking. CoP towards the big toe during single support to reduce the amount of hip sway. A similar approach is proposed here to improve stability on compliant terrain. As illustrated in Fig. 4, a lateral offset is introduced to shift the CoP toward the inside of the support foot. This decreases the lateral motion of the CoM similar to narrowing the step width, yet without the additional risk of self-collision. By increasing the nominal distance of the CoP to the outer edge of the foot, additional horizontal torque is available to correct for DCM overshoot. This decreases the risk of outward tipping. In the event of inward tipping, the controller can still regain stability through an appropriate step adjustment. B. Stairs Task The DRC course featured an industrial stairway and rough terrain area designed to test the robot s mobility in structured and unstructured environments. The team chose to focus development efforts on the stairs task rather than the rough terrain, due to initial range of motion issues encountered while stepping down on the cinder blocks. Although the proposed controls approach was designed to support locomotion on uneven terrain, a number of difficulties arose during the course of testing due to the risk of collision between the support leg and upper stair when stepping up. In order to increase the available workspace, a half-step strategy was adopted, permitting the robot to place the center of the support foot on the lip of the stair. As illustrated in Fig. 5, the rear contact points were shifted to the middle of the sole in order to appropriately constrain the CoP trajectory. To prevent knee and shin collisions, a soft position limit was enforced on the ankle pitch joint corresponding to the measured angle of collision. Using this approach, the inverse dynamics optimization was able to appropriately adjust the ankle pitch to avoid collision during stepping. By reducing the available ankle range of motion, careful design of the nominal CoM height trajectory was required to enable the robot to safely step onto the stair. Fig. 5 includes the vertical CoM and DCM reference trajectories corresponding to a 23 cm (9 in) step. Note that the CoM begins to accelerate at the beginning of the double support phase. Raising the CoM height early in the step cycle tends to rotate the support ankle away from the soft position limit. This has the added benefit of straightening the support knee, resulting in lower knee torques. As the CoM height increases, the length of the swing leg also increases. As a result, significant toe-off is required to allow the foot to remain in contact with the stair prior to lift-off. Fig. 5. Left: A half-step strategy is implemented to increase the available collision-free workspace of the support leg when ascending stairs. Right: During ascension, vertical CoM acceleration initiates at the beginning of the double support phase (shaded in gray), reducing the required knee torque. VI. EXPERIMENTAL RESULTS This section presents experimental results for the ESCHER humanoid demonstrating the walking controller s ability to negotiate each of the challenges discussed in the previous section. Identical control parameters are used in each experiment (refer to Table I), with the exception of the stairs task which required stiffer tracking of the z-axis DCM trajectory. A. Soft and Uncertain Terrain Images of ESCHER walking on a various indoor and outdoor terrain including grass, gravel, dirt, and unmodeled blocks can be seen in Fig. 6. Compliant control of the lower body enables accurate tracking of the desired ground reaction forces, allowing the robot to adapt naturally to uncertain terrain features. Figure 7 includes the desired and estimated horizontal CoP, VRP, and DCM trajectories corresponding to two separate walking experiments conducted on 3.5 cm pile height artificial turf (refer to Fig. 6-a). In the first experiment, the desired CoP waypoints are shifted by 2 cm towards in the inside of the foot as described in Section V-A. In the second experiment, the CoP waypoints are defined at the center of the support foot. In each case, the desired footstep plan consists of eight forward steps with a stride length of 0.15 m, step duration of 2 s, double support time of 0.6 s and single support time of 1.4 s. The results demonstrate that the lateral CoP offset can significantly reduce oscillations in the VRP, DCM, and CoP trajectories resulting from unmodeled surface compliance. Note that, without the offset, the estimated CoP approaches the edge of the foot on multiple occasions, indicating that the robot is approaching a tipping point. Fig. 6. ESCHER walking on various terrain including grass, gravel, and 3.8 cm blocks. In each case, the controller assumes a rigid contact surface, and has no knowledge of height variations or surface compliance.

6 Fig. 8. Time-lapse of ESCHER stepping up onto a 23 cm x 28 cm block, representative of the stairs task at the DRC Finals. Fig. 7. Desired and estimated DCM, VRP, and CoP trajectories while walking on artificial turf with a 2 s step duration. In the top plot, the CoP trajectory is shifted inward by 2 cm to improve tracking performance. In the bottom plot, the CoP passes through the center of the foot. B. Uneven Terrain Figure 8 includes images of the robot stepping onto a set of cinder blocks with the same height and depth as the industrial stairs in the DRC Finals course (23 cm x 28 cm). Image 3a and 3b were captured during toe-off, as the robot pitched the right ankle to extend the effective length of the swing leg. In this experiment, the heel of the left foot was positioned 10 cm from the lip of the stair. With 60% of the sole in contact, this configuration provided a slight safety margin to prevent the foot from rocking given the limited base of support. Note that the support bar on the knee clears the upper stair by approximately 2 cm using the methods described in Section V-B. A minimum position limit of 0.6 radians was selected for the ankle pitch joint in order to prevent collision. For this experiment, the proportional gain of the DCM controller was increased from 3 m/m to 5 m/m in the vertical axis, while the vertical l d weighting was increased from 1 to 5 to improve tracking (refer to Table I). C. Step Adjustment In a final experiment, ESCHER was subjected to external disturbance forces while walking forward on flat terrain. Figure 10 includes the lateral CoM, VRP, and DCM trajectories over the course of eight steps. The figure marks the desired horizontal position of the swing foot at the time of heelstrike to illustrate the corresponding step adjustments. As in the compliant terrain experiments, each footstep was selected with a 2 s step duration and 0.15 m stride length to emulate a moderate walking speed. Two disturbance impulses of increasing magnitude were applied at approximately 6 and 10 seconds. Figure 9 includes a time lapse of the robot recovering from the large push applied to the left hip using the proposed step adjustment strategy (5). As illustrated in Fig. 10, each push results in a significant deviation of the estimated DCM from the nominal reference trajectory. The DCM error transients appearing in the Fig. 9. Time-lapse of a lateral step adjustment in response to an external disturbance applied to the hip (corresponding to Fig. 10 at the 10 s mark). Fig. 10. Lateral DCM, VRP, and CoM trajectories during step adjustment experiment. The desired swing foot position at the time of each heel strike is noted by the triangle markers (blue for nominal, yellow for adjusted reference). The two lateral pushes occur at approximately 6 and 10 seconds. undisturbed steps occur primarily during heel-strike and are quickly corrected by the momentum controller. The DCM error transient following the first push is within the deadband of the step adjustment algorithm. Thus, the desired foothold position remains unchanged, as the momentum controller is able to eliminate the error by shifting the ecmp. The second push, however, results in an error that exceeds the deadband, triggering a step adjustment of 6.8 cm in the same direction as the disturbance force. The modified base of support allows the robot to apply the necessary restoring forces to stabilize the DCM following heel-strike. Note that the DCM tracking quality is recovered within one step.

7 VII. CONCLUSION The experimental results demonstrated the effectiveness of the proposed controls approach for locomotion on soft and uneven terrain. By shifting the nominal CoP trajectory towards the inside of the foot, the controller was able to reduce lateral sway and improve tracking performance in the presence of unknown surface features. This simple modification was critical to the robot s ability to walk on outdoor surfaces including dirt, gravel, and grass. The proposed step adjustment algorithm was shown to increase controller robustness in the presence of external disturbances. The results motivate the use of simple heuristics to modify the swing foot position in response to the estimated DCM error. The proposed walking controller was used during the DRC Finals without modification. On the first day, the robot fell when traversing the 200 ft dirt track due to a minor hardware complication. On the second day, the robot was able to walk from the starting line to the door, verifying the reliability of the proposed approach on compliant terrain. Additional experiments were performed using identical control parameters on a variety of terrain to test the reliability of the approach. Although unable to attempt the stairs task at the DRC Finals, ESCHER successfully demonstrated the proposed approach outside of competition. The use of a half-step strategy significantly increased the available workspace. When combined with careful vertical CoM planning, a soft position limit on the ankle joint allowed the robot to avoid collisions in a natural fashion when stepping up. Future research efforts will focus on alternative methods for real-time step adjustment using model predictive control. Additional efforts will investigate optimization-based methods to generate the nominal CoM height trajectory on uneven terrain. ACKNOWLEDGMENTS This material is supported by ONR through grant N and by DARPA through grant N We would like to thank the DRC competition team and all of the students who contributed to the development of ESCHER. REFERENCES [1] M. A. Hopkins, D. W. Hong, and A. Leonessa, Compliant locomotion using whole-body control and Divergent Component of Motion tracking, in Robotics and Automation (ICRA), IEEE International Conference on, May [2] M. A. Hopkins, D. W. Hong, and A. Leonessa, Humanoid locomotion on uneven terrain using the time-varying Divergent Component of Motion, in Humanoid Robots (Humanoids), 14th IEEE-RAS International Conference on, Nov [3] M. A. Hopkins, S. A. Ressler, D. F. Lahr, D. W. Hong, and A. Leonessa, Embedded joint-space control of a series elastic humanoid, in Intelligent Robots and Systems (IROS), IEEE/RSJ International Conference on, Hamburg, Germany, October [4] S. Feng, E. Whitman, X. Xinjilefu, and C. G. 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