Michel Taïx

Steve Tonneau, Daeun Song, Pierre Fernbach et al.

One 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.

Andreas Orthey, Olivier Roussel, Olivier Stasse et al.

The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce the dimensionality of the configuration space by introducing the irreducible path --- a path having a minimal swept volume. The paper consists of three parts: In part I, we define the space of all irreducible paths and show that planning a path in the irreducible path space preserves completeness of any motion planning algorithm. In part II, we construct an approximation to the irreducible path space of a serial kinematic chain under certain assumptions. In part III, we conduct motion planning using the irreducible path space for a mechanical snake in a turbine environment, for a mechanical octopus with eight arms in a pipe system and for the sideways motion of a humanoid robot moving through a room with doors and through a hole in a wall. We demonstrate that the concept of an irreducible path can be applied to any motion planning algorithm taking curvature constraints into account.