Online adaptation of reference trajectories for the control of walking systems

International audienceA simple and widely used way to make a robotic system walk without falling is to make it track a reference tra jectory in one way or another, but the stability obtained this way may be limited and even small perturbations may lead to a fall. We propose here a series of heuristics to improve the stability that can be obtained from such a tracking control law, through an online adaptation of the choice of the reference tra jectory being tracked. Encouraging simulations are obtained in the end on a simple planar biped model

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

Model Predictive Control

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On the stability of walking systems

International audienceWe reconsider here the stability criteria usually proposed for the analysis of walking systems, exhibiting their limits and their ambiguity. We propose then some new criteria based on a thorough analysis of the dynamics of walking systems and precise definitions concerning their stability. Numerical methods are presented then to deal with these new criteria

Some comments on the structure of the dynamics of articulated motion

International audienceWalking, running or jumping are special cases of articulated motions which rely heavily on contact forces for their accomplishment. This central role of the contact forces is widely recognized now, but it is rarely connected to the structure of the dynamics of articulated motion. Indeed, this dynamics is generally considered as a complex nonlinear black-box without any specific structure, or its structure is only partly uncovered. We propose here to precise this structure and show in details how it shapes the movements that an articulated system might realize. Some propositions are made then to improve the design of control laws for walking, running, jumping or free-floating motions

Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations

International audienceA humanoid walking robot is a highly nonlinear dynamical system that relies strongly on contact forces between its feet and the ground in order to realize stable motions, but these contact forces are unfortunately severely limited. Model Predictive Control, also known as Receding Horizon Control, is a general control scheme specifically designed to deal with such contrained dynamical systems, with the potential ability to react efficiently to a wide range of situations. Apart from the question of computation time which needs to be taken care of carefully (these schemes can be highly computation intensive, the initial question of which optimal control problems should be considered to be solved online in order to lead to the desired walking movements is still unanswered. A key idea for answering to this problem can be found in the ZMP Preview Control scheme. After presenting here this scheme with a point of view slightly different from the original one, we focus on the problem of compensating strong perturbations of the dynamics of the robot and propose a new Linear Model Predictive Control scheme which is an improvement of the original ZMP Preview Control scheme

Constrained dynamics and parametrized control in biped walking

International audienceThe intermittent contact with the ground is the main speci- ficity of walking robots, allowing more versatility in their displacements, but resulting in a structural instability of these systems. A walking robot, having a free-floating base, can- not control its global movements directly and must rely on the limited interaction forces in order to move. These con- straints on the movements of the robot are an obstacle to the stabilization of a trajectory. We propose then to stabilize not a single trajectory but a parametrized set qd (t, p) of all the possible trajectories, depending on the lentgth of the steps, the speed of execution... The idea is that a destabilization can be compensated by an adaptation of the walk

Efficient resolution of potentially conflicting linear constraints in robotics

Submitted to IEEE TRO (05/August/2015)—A classical approach to handling potentially conflicting linear equality and inequality constraints in robotics is to impose a strict prioritization between them. Ensuring that the satisfaction of constraints with lower priority does not impact the satisfaction of constraints with higher priority is routinely done by solving a hierarchical least-squares problem. Such a task prioritization is often considered to be computationally demanding and, as a result, it is often approximated using a standard weighted least-squares problem. The main contribution of this article is to address this misconception and demonstrate, both in theory and in practice, that the hierarchical problem can in fact be solved faster than its weighted counterpart. The proposed approach to efficiently solving hierarchical least-squares problems is based on a novel matrix factorization, to be referred to as " lexicographic QR " , or ℓ-QR in short. We present numerical results based on three representative examples adopted from recent robotics literature which demonstrate that complex hierarchical problems can be tackled in real-time even with limited computational resources

Efficient resolution of potentially conflicting linear constraints in robotics

Submitted to IEEE TRO (05/August/2015)—A classical approach to handling potentially conflicting linear equality and inequality constraints in robotics is to impose a strict prioritization between them. Ensuring that the satisfaction of constraints with lower priority does not impact the satisfaction of constraints with higher priority is routinely done by solving a hierarchical least-squares problem. Such a task prioritization is often considered to be computationally demanding and, as a result, it is often approximated using a standard weighted least-squares problem. The main contribution of this article is to address this misconception and demonstrate, both in theory and in practice, that the hierarchical problem can in fact be solved faster than its weighted counterpart. The proposed approach to efficiently solving hierarchical least-squares problems is based on a novel matrix factorization, to be referred to as " lexicographic QR " , or ℓ-QR in short. We present numerical results based on three representative examples adopted from recent robotics literature which demonstrate that complex hierarchical problems can be tackled in real-time even with limited computational resources