Safe 3D Bipedal Walking through Linear MPC with 3D Capturability

International audienceWe propose a linear MPC scheme for online computation of reactive walking motions, necessary for fast interactions such as physical collaboration with humans or collision avoidance in crowds. Unlike other existing schemes, it provides fully adaptable height, adaptable step placement and complete kinematic and dynamic feasibility guarantees, making it possible to walk perfectly safely on a piecewise horizontal ground such as stairs. A linear formulation is proposed, based on efficiently bounding the nonlinear term introduced by vertical motion, considering two linear constraints instead of one nonlinear constraint. Balance and Passive Safety guarantees are secured by enforcing a 3D capturability constraint. Based on a comparison between CoM and CoP trajectories involving exponentials instead of polynomials, this capturability constraint involves a CoM motion stopping along a segment of line, always maintaining complete kinematic and dynamic feasibility

C-CROC: Continuous and Convex Resolution of Centroidal Dynamic Trajectories for Legged Robots in Multicontact Scenarios

International audienceSynthesizing legged locomotion requires planning one or several steps ahead (literally): when and where, and with which effector shouldthe next contact(s) be created between the robot and the environment? Validating a contact candidate implies \textit{a minima} the resolution of a slow, non-linear optimizationproblem, to demonstrate that a Center Of Mass (COM) trajectory, compatible with the contact transition constraints, exists. We propose a conservative reformulation of this trajectory generation problem as a convex 3D linear program, CROC. It results from the observation that if the COM trajectory is a polynomial with only one free variable coefficient, the non-linearity of the problem disappears. This has two consequences. On the positive side, in terms of computation times CROC outperforms the state of the art by at least one order of magnitude, and allows to consider interactive applications (with a planning time roughly equal to the motion time). On the negative side, in our experiments our approach finds a majority of the feasible trajectories found by a non-linear solver, but not all of them. Still, we demonstrate that the solution space covered by CROC is large enough to achieve the automated planning of a large variety of locomotion tasks for different robots, demonstrated in simulation and on the real HRP-2 robot, several of which were rarely seen before.Another significant contribution is the introduction of a Bezier curve representation of the problem, which guarantees that the constraints of the COM trajectory are verified continuously, and not only at discrete points as traditionally done. This formulation is lossless, and results in more robust trajectories. It is not restricted to CROC, but could rather be integrated with any method from the state of the art

Recent Progress in Legged Robots Locomotion Control

International audiencePurpose of review. In recent years, legged robots locomotion has been transitioning from mostly flat ground in controlled settings to generic indoor and outdoor environments, approaching now real industrial scenarios. This paper aims at documenting some of the key progress made in legged locomotion control that enabled this transition. Recent findings. Legged locomotion control makes extensive use of numerical trajectory optimization and its online implementation, Model Predictive Control. A key progress has been how this optimization is handled, with refined models and refined numerical methods. This led the legged locomotion research community to heavily invest in and contribute to the development of new optimization methods and efficient numerical software

Solving Footstep Planning as a Feasibility Problem Using L1-Norm Minimization

Extended version of the paper to be published in IEEE Robotics and Automation LettersInternational audienceOne challenge of legged locomotion on uneven terrains is to deal with both the discrete problem of selecting a contact surface for each footstep and the continuous problem of placing each footstep on the selected surface. Consequently, footstep planning can be addressed with a Mixed Integer Program (MIP), an elegant but computationally-demanding method, which can make it unsuitable for online planning. We reformulate the MIP into a cardinality problem, then approximate it as a computationally efficient l1-norm minimisation, called SL1M. Moreover, we improve the performance and convergence of SL1M by combining it with a sampling-based root trajectory planner to prune irrelevant surface candidates. Our tests on the humanoid Talos in four representative scenarios show that SL1M always converges faster than MIP. For scenarios when the combinatorial complexity is small (< 10 surfaces per step), SL1M converges at least two times faster than MIP with no need for pruning. In more complex cases, SL1M converges up to 100 times faster than MIP with the help of pruning. Moreover, pruning can also improve the MIP computation time. The versatility of the framework is shown with additional tests on the quadruped robot ANYmal

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

Legged Robots

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Impact-Aware Multi-Contact Balance Criteria

Intentionally applying impacts while maintaining balance is challenging for legged robots. This study originated from observing experimental data of the humanoid robot HRP-4 intentionally hitting a wall with its right arm while standing on two feet. Strangely, violating the usual zero moment point balance criteria did not systematically result in a fall. To investigate this phenomenon, we propose the zero-step capture region for non-coplanar contacts, defined as the center of mass (CoM) velocity area, and validated it with push-recovery experiments employing the HRP-4 balancing on two non-coplanar contacts. To further enable on-purpose impacts, we compute the set of candidate post-impact CoM velocities accounting for frictional-impact dynamics in three dimensions, and restrict the entire set within the CoM velocity area to maintain balance with the sustained contacts during and after impacts. We illustrate the maximum contact velocity for various HRP-4 stances in simulation, indicating potential for integration into other task-space whole-body controllers or planners. This study is the first to address the challenging problem of applying an intentional impact with a kinematic-controlled humanoid robot on non-coplanar contacts