Adrien Escande

Stéphane Caron, Adrien Escande, Leonardo Lanari et al.

Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on the capture point. We generalize this analysis to the variable-height inverted pendulum (VHIP) and show how it enables 3D walking over uneven terrains based on capture inputs. Thanks to a tailored optimization scheme, we can compute these inputs fast enough for real-time model predictive control. We implement this approach as open-source software and demonstrate it in dynamic simulations.

Kai Pfeiffer, Adrien Escande, Ludovic Righetti

Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the higher priority levels. Active-set methods are a popular choice for solving them. However, they can perform poorly in terms of computational time if there are large changes of the active set. We therefore propose a computationally efficient primal-dual interior-point method (IPM) for dense HLSP's which is able to maintain constant numbers of solver iterations in these situations. We base our IPM on the computationally efficient nullspace method as it requires only a single matrix factorization per solver iteration instead of two as it is the case for other IPM formulations. We show that the resulting normal equations can be expressed in least-squares form. This avoids the formation of the quadratic Lagrangian Hessian and can possibly maintain high levels of sparsity. Our solver reliably solves ill-posed instantaneous hierarchical robot control problems without exhibiting the large variations in computation time seen in active-set methods.

Andreas Orthey, Adrien Escande, Eiichi Yoshida

A motion planning algorithm computes the motion of a robot by computing a path through its configuration space. To improve the runtime of motion planning algorithms, we propose to nest robots in each other, creating a nested quotient-space decomposition of the configuration space. Based on this decomposition we define a new roadmap-based motion planning algorithm called the Quotient-space roadMap Planner (QMP). The algorithm starts growing a graph on the lowest dimensional quotient space, switches to the next quotient space once a valid path has been found, and keeps updating the graphs on each quotient space simultaneously until a valid path in the configuration space has been found. We show that this algorithm is probabilistically complete and outperforms a set of state-of-the-art algorithms implemented in the open motion planning library (OMPL).

Silvio Traversaro, Stanislas Brossette, Adrien Escande et al.

This paper presents a new condition, the fully physical consistency for a set of inertial parameters to determine if they can be generated by a physical rigid body. The proposed condition ensure both the positive definiteness and the triangular inequality of 3D inertia matrices as opposed to existing techniques in which the triangular inequality constraint is ignored. This paper presents also a new parametrization that naturally ensures that the inertial parameters are fully physical consistency. The proposed parametrization is exploited to reformulate the inertial identification problem as a manifold optimization problem, that ensures that the identified parameters can always be generated by a physical body. The proposed optimization problem has been validated with a set of experiments on the iCub humanoid robot.