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

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

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

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

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

Contribution à la planification de mouvements en robotique

Les travaux présentés dans ce manuscrit d'Habilitation à Diriger des Recherches concernent la problématique de la planification de trajectoires pour un système robotique. Nous présentons des méthodes et des algorithmes qui calculent automatiquement des trajectoires géométriques sans collision et qui prennent en compte les contraintes du système pour effectuer une tâche. Dans une première partie, nous nous intéressons aux robots mobiles à roues. Nous avons développé une algorithmique pour calculer, si elle existe, une trajectoire pour un robot articulé en terrain accidenté qui garantit les contraintes de validité (stabilité, contraintes mécaniques et non collision). Afin d'améliorer la robustesse de notre approche, il est apparu nécessaire de prendre en compte le lien entre planification, localisation et exécution. Nous proposons une méthode pour définir automatiquement les amers pertinents à sélectionner le long de la trajectoire et étudions les conditions de leurs enchaînements. Nous transformons ainsi une planification de trajectoire géométrique en une suite de tâches référencées capteurs. Nous nous sommes ensuite intéressés au problème de recouvrement de surface pour lequel c'est la tâche robotique qui amène à définir implicitement une trajectoire. Nous avons développé une nouvelle approche incluant la gestion automatique des zones de fourrière. Dans une deuxième partie, nous avons étendu la problématique hors du champ de la robotique à roues. Nous avons commencé par combiner les avantages de différentes techniques de planification probabiliste afin de résoudre plus e cacement le problème des passages étroits. Il est alors apparu intéressant de faire coopérer un opérateur humain avec un algorithme de recherche probabiliste. Nous proposons une variante basée sur les Rapidly-exploring Random Trees pour construire un RRT-Interactif qui améliore le guidage d'un opérateur lors d'une tâche d'assemblage dans un environnement virtuel. Pour mieux comprendre le mouvement h umain, nous avons appliqué des principes moteurs neurobiologiques pour le contrôle du geste d'atteinte des robots humanoïdes. Nous montrons que cette approche permet de générer des mouvements réalistes qui respectent les caractéristiques du mouvement humain et qu'il est ensuite possible de synthétiser les mouvements d'atteinte par une combinaison de primitives motrices. Pour conclure, il nous semble intéressant d'étendre nos travaux, d'une part en planifiant des mouvements réalistes par rapport au mouvement humain en vue de l'introduction de mannequins numériques ; d'autre part, en planifiant des mouvements pour des objets déformables car de nombreux problèmes pratiques ne peuvent pas être résolus en considérant des objets rigides

Deformable Linear Object manipulation planning with contacts

International audienceWe consider the manipulation planning problem of a Deformable Linear Object (DLO) in free or contact space. We assume the DLO is handled by a gripper at one of its extremities and during the manipulating phase, the grasped end may change. The problem is solved by coupling dynamic simulation for the DLO and kinodynamic motion planning with contacts. We show the necessity of considering contacts for this type of problem with several simulation experiments by comparing with classical collision-free approaches

Robotics, Mechatronics and Product Engineering

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Motion Planning with interactive devices

International audienceThis paper presents interaction between a user and a robot to guide motion through motion planning algorithm. The interaction aims at improving the guidance of an operator during a robot motion task in a virtual environment with the help of an automatic path planning algorithm. Existing works use a twostep decomposition which limits the interaction between the user and the ongoing process. We propose a modification of a classic motion planning method, the Rapidly-exploring Random Tree to build a Interactive-RRT. This method is based on exchanging forces between the algorithm and the user, and on data gathering (labels) from the virtual scene. Examples are shown to illustrate the Interactive motion planning system and analysis are done in function on the user's dexterity to manipulate devices