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

Learning How to Walk: Warm-starting Optimal Control Solver with Memory of Motion

In this paper, we propose a framework to build a memory of motion for warm-starting an optimal control solver for the locomotion task of a humanoid robot. We use HPP Loco3D, a versatile locomotion planner, to generate offline a set of dynamically consistent whole-body trajectory to be stored as the memory of motion. The learning problem is formulated as a regression problem to predict a single-step motion given the desired contact locations, which is used as a building block for producing multi-step motions. The predicted motion is then used as a warm-start for the fast optimal control solver Crocoddyl. We have shown that the approach manages to reduce the required number of iterations to reach the convergence from ~9.5 to only ~3.0 iterations for the single-step motion and from ~6.2 to ~4.5 iterations for the multi-step motion, while maintaining the solution's quality

Motion Planning for Multi-Contact Visual Servoing on Humanoid Robots

International audienceThis paper describes the implementation of a canonical motion generation pipeline guided by vision for a TALOS humanoid robot. The proposed system is using a mul-ticontact planner, a Differential Dynamic Programming (DDP) algorithm, and a stabilizer. The multicontact planner provides a set of contacts and dynamically consistent trajectories for the Center-Of-Mass (CoM) and the Center-Of-Pressure (CoP). It provides a structure to initialize a DDP algorithm which, in turn, provides a dynamically consistent trajectory for all the joints as it integrates all the dynamics of the robot, together with rigid contact models and the visual task. Tested on Gazebo the resulting trajectory had to be stabilized with a state-of-the-art algorithm to be successful. In addition to testing motion generated from high specifications to the stabilized motion in simulation, we express visual features at Whole Body Generator level which is a DDP formulated solver. It handles non-linearities as the ones introduced by the projections of visual features expressed and minimized in the image plan of the camera

SL1M: Sparse L1-norm Minimization for contact planning on uneven terrain

International audienceOne of the main challenges of planning legged locomotion in complex environments is the combinatorial contact selection problem. Recent contributions propose to use integer variables to represent which contact surface is selected, and then to rely on modern mixed-integer (MI) optimization solvers to handle this combinatorial issue. To reduce the computational cost of MI, we exploit the sparsity properties of L1 norm minimization techniques to relax the contact planning problem into a feasibility linear program. Our approach accounts for kinematic reachability of the center of mass (COM) and of the contact effectors. We ensure the existence of a quasi-static COM trajectory by restricting our plan to quasi-flat contacts. For planning 10 steps with less than 10 potential contact surfaces for each phase, our approach is 50 to 100 times faster that its MI counterpart, which suggests potential applications for online contact re-planning. The method is demonstrated in simulation with the humanoid robots HRP-2 and Talos over various scenarios

Torque Controlled Locomotion of a Biped Robot with Link Flexibility

When a big and heavy robot moves, it exerts large forces on the environment and on its own structure, its angular momentum can varysubstantially, and even the robot's structure can deform if there is a mechanical weakness. Under these conditions, standard locomotion controllers can fail easily. In this article, we propose a complete control scheme to work with heavy robots in torque control. The full centroidal dynamics is used to generate walking gaits online, link deflections are taken into account to estimate the robot posture and all postural instructions are designed to avoid conflicting with each other, improving balance. These choices reduce model and control errors, allowing our centroidal stabilizer to compensate for the remaining residual errors. The stabilizer and motion generator are designed together to ensure feasibility under the assumption of bounded errors. We deploy this scheme to control the locomotion of the humanoid robot Talos, whose hip links flex when walking. It allows us to reach steps of 35~cm, for an average speed of 25~cm/sec, which is among the best performances so far for torque-controlled electric robots.Comment: IEEE-RAS International Conference on Humanoid Robots (Humanoids 2022), IEEE, Nov 2022, Ginowan, Okinawa, Japa

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

Whole Body Model Predictive Control with a Memory of Motion: Experiments on a Torque-Controlled Talos

This paper presents the first successful experiment implementing whole-body model predictive control with state feedback on a torque-control humanoid robot. We demonstrate that our control scheme is able to do whole-body target tracking, control the balance in front of strong external perturbations and avoid collision with an external object. The key elements for this success are threefold. First, optimal control over a receding horizon is implemented with Crocoddyl, an optimal control library based on differential dynamics programming, providing state-feedback control in less than 10 msecs. Second, a warm start strategy based on memory of motion has been implemented to overcome the sensitivity of the optimal control solver to initial conditions. Finally, the optimal trajectories are executed by a low-level torque controller, feedbacking on direct torque measurement at high frequency. This paper provides the details of the method, along with analytical benchmarks with the real humanoid robot Talos

Modèles réduits fiables et efficaces pour la planification et l'optimisation de mouvement des robots à pattes en environnements contraints

The automatic synthesis of movements for legged robots is one of the long standing challenge of robotics, and its resolution is a prior to the safe deployment of robots outside of their labs. In this thesis, we tackle it with a divide and conquer approach, where several smaller sub-problems are identified and solved sequentially to generate motions in a computationally efficient manner. This decoupling comes with a feasibility issue : how can we guarantee that the solution of a sub-problem is a valid input for the next sub-problem ? To address this issue, this thesis defines computationally efficient feasibility criteria, focused on the constraints on the Center Of Mass of the robot. Simultaneously, it proposes a new formulation of the problem of computing a feasible trajectory for the Center Of Mass of the robot, given a contact sequence. This formulation is continuous, as opposed to traditional approaches that rely on a discretized formulation, which can result in constraint violations and are less computationally efficient. This general formulation could be straightforwardly used with any existing approach of the state of the art. The framework obtained was experimentally validated both in simulation and on the HRP-2 robot, and presented a higher success rate, as well as computing performances order of magnitudes faster than the state of the art.La synthèse automatique du mouvement de robots à pattes est un enjeu majeur de la robotique: sa résolution permettrait le déploiement des robots hors de leurs laboratoire. Pour y parvenir, cette thèse suit l'approche "diviser pour régner", où le problème est décomposé en plusieurs sous-problèmes résolus séquentiellement. Cette décomposition amène alors la question nouvelle de la faisabilité: comment garantir que la solution d'un sous-problème, permet la résolution des suivants (dont elle sert d'entrée)? Pour y répondre, cette thèse définit des critères de faisabilités efficaces, qui s'appuient sur la définition des contraintes qui s'appliquent au centre de masse du robot. En parallèle, et de manière plus générale, elle propose une nouvelle formulation du problème du calcul d'une trajectoire valide pour le centre de masse du robot. Cette formulation, continue, présente le double avantage (par rapport aux méthodes discrètes classiques) de garantir la validité de la solution en tous points, tout en améliorant, grâce à une réduction de la dimensionnalité du problème, les performances des algorithmes de l'état de l'art. L'architecture de planification de mouvement résultante a été validée en simulation, ainsi que sur le robot HRP-2, démontrant ainsi sa supériorité en termes de temps de calcul et de taux de succès par rapport à l'existant