Whole-body Control (WBC) has emerged as an important framework in locomotion control for legged robots. However, most of WBC frameworks fail to generalize beyond rigid terrains. Legged locomotion over soft terrain is difficult due to the presence of unmodeled contact dynamics that WBCs do not account for. This introduces uncertainty in locomotion and affects the stability and performance of the system. In this paper, we propose a novel soft terrain adaptation algorithm called STANCE: Soft Terrain Adaptation and Compliance Estimation. STANCE consists of a WBC that exploits the knowledge of the terrain to generate an optimal solution that is contact consistent and an online terrain compliance estimator that provides the WBC with terrain knowledge. We validated STANCE both in simulation and experiment on the Hydraulically actuated Quadruped (HyQ) robot, and we compared it against the state of the art WBC. We demonstrated the capabilities of STANCE with multiple terrains of different compliances, aggressive maneuvers, different forward velocities, and external disturbances. STANCE allowed HyQ to adapt online to terrains with different compliances (rigid and soft) without pre-tuning. HyQ was able to successfully deal with the transition between different terrains and showed the ability to differentiate between compliances under each foot.
In contrast to the aforementioned work, other approaches relax the rigid ground assumption (hard contact constraint) but not for soft terrain adaptation purposes. For instance, Kim al @cite_5 implemented an approach to handle sudden changes in the rigid contact interaction. This approach relaxed the hard contact assumption in their wbc formulation by penalizing the contact interaction in the cost function rather than incorporating it as a hard constraint. For computational purposes, Neunert al @cite_26 and Doshi al @cite_14 proposed relaxing the rigid ground assumption. Neunert al used a soft contact model in their nonlinear mpc formulation to provide smooth gradients of the contact dynamics to be more efficiently solved by their gradient based solver. The soft contact model did not have a physical meaning and the contact parameters were empirically chosen. Doshi al proposed a similar approach which incorporates a slack variable that expands the feasibility region of the hard constraint.
@cite_5 @cite_14 @cite_26
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Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this paper, we devise a new WBC, dubbed whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints such that the control commands produce reduced jerk when switching foot contacts. To achieve robust dynamic locomotion, we conduct an in-depth analysis of uncertainty for our dynamic walking algorithm called time-to-velocity-reversal (TVR) planner. The uncertainty study is fundamental as it allows us to improve the control algorithms and mechanical structure of our robot to fulfill the tolerated uncertainty. In addition, we conduct extensive experimentation for: 1) unsupported dynamic balancing (i.e. in-place stepping) with a six degree-of-freedom (DoF) biped, Mercury; 2) unsupported directional walking with Mercury; 3) walking over an irregular and slippery terrain with Mercury; and 4) in-place walking with our newly designed ten-DoF viscoelastic liquid-cooled biped, DRACO. Overall, the main contributions of this work are on: a) achieving various modalities of unsupported dynamic locomotion of passive-ankle bipeds using a WBLC controller and a TVR planner, b) conducting an uncertainty analysis to improve the mechanical structure and the controllers of Mercury, and c) devising a whole-body control strategy that reduces movement jerk during walking. Planning locomotion trajectories for legged microrobots is challenging because of their complex morphology, high frequency passive dynamics, and discontinuous contact interactions with their environment. Consequently, such research is often driven by time-consuming experimental methods. As an alternative, we present a framework for systematically modeling, planning, and controlling legged microrobots. We develop a three-dimensional dynamic model of a 1.5 gram quadrupedal microrobot with complexity (e.g., number of degrees of freedom) similar to larger-scale legged robots. We then adapt a recently developed variational contact-implicit trajectory optimization method to generate feasible whole-body locomotion plans for this microrobot, and we demonstrate that these plans can be tracked with simple joint-space controllers. We plan and execute periodic gaits at multiple stride frequencies and on various surfaces. These gaits achieve high per-cycle velocities, including a maximum of 10.87 mm cycle, which is 15 faster than previously measured velocities for this microrobot. Furthermore, we plan and execute a vertical jump of 9.96 mm, which is 78 of the microrobot's center-of-mass height. To the best of our knowledge, this is the first end-to-end demonstration of planning and tracking whole-body dynamic locomotion on a millimeter-scale legged microrobot. In this letter, we present a whole-body nonlinear model predictive control approach for rigid body systems subject to contacts. We use a full-dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences, and timings are not prespecified but optimized by the solver. Yet, using numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state-of-the-art by at least one order of magnitude. Hardware experiments in the form of periodic and nonperiodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability, and robustness of the approach.