Identification of Fully Physical Consistent Inertial Parameters using Optimization on Manifolds

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.Comment: 6 pages, published in Intelligent Robots and Systems (IROS), 2016 IEEE/RSJ International Conference o

Multi-Contact Postures Computation on Manifolds

International audienceWe propose a framework to generate static robot configurations satisfying a set of physical and geometrical constraints. This is done by formulating nonlinear constrained optimization problems over non-Euclidean manifolds and solving them. To do so, we present a new sequential quadratic programming (SQP) solver working natively on general manifolds, and propose an interface to easily formulate the problems, with the tedious and error-prone work automated for the user. We also introduce several new types of constraints for having more complex contacts or working on forces/torques. Our approach allows an elegant mathematical description of the constraints and we exemplify it through formulation and computation examples in complex scenarios with humanoid robots

Vertical ladder climbing by the HRP-2 humanoid robot

International audienceWe report the results obtained from our trials in making the HRP-2 humanoid robot climb vertical industrial-norm ladders. We integrated our multi-contact planner and multi-objective QP control as basic components. First, a set of contacts to climb the ladder is planned off-line and provided as an input for a finite state machine that sequences tasks to be realized by our multi-objective model-based QP in closed-loop control. The trials we made revealed that hardware changes are to be made on the HRP-2, and the software has to be made more robust. Yet, we confirmed that HRP-2 has power capability to climb real industrial ladders, such as those found in nuclear power plants and large scale manufacturings (e.g. airliners, shipyards and buildings)

Viable Multi-Contact Posture Computation for Humanoid Robots using Nonlinear Optimization on Manifolds

Humanoid robots are complex poly-articulated structures with nonlinear kinematics and dynamics. Finding viable postures to realize set-point task objectives under a set of constraints (intrinsic and extrinsic limitations) is a key issue in the planning of robot motion and animportant feature of any robotics framework. It is handled by the so called posture generator (PG) that consists in formalizing the viable posture as the solution to a nonlinear optimization problem. We present several extensions to the state-of-the-art by exploring new formulationsand resolution methods for posture generation problems. We reformulate the notion of contact constraints by adding variables to enrich the optimization problem and allow the solver to decide the shape of intersection of contact polygons, or of the location of a contactpoint on a non-flat surface. We present a reformulation of the posture generation problem that encompasses non-Euclidean manifolds natively and presents a more elegant and efficient mathematical formulation of it. To solve such problems, we implemented a new SQP solver that is particularly suited to handle non-Euclidean manifolds structures. By doing so, we have a better mastering in the way to tune and specialize our solver for robotics problems.Un robot humanoïde est un système poly-articulé complexe dont la cinématique et la dynamique sont gouvernées par des équations non-linéaires. Trouver des postures viables qui minimizent une tâche objectif tout en satisfaisant un ensemble de contraintes (intrinsèques ou extrinsèques) est un problème central pour la planification de mouvement robotique et est une fonctionnalité importante de tout logiciel de robotique. Le générateur de posture (PG) a pour rôle de trouver une posture viable en formulant puis résolvant un problème d’optimisation non-linéaire. Nous étendons l’état de l’art en proposant de nouvelles formulations et méthodes de résolution de problèmes de génération de posture. Nous enrichissons la formulation de contraintes de contact par ajout de variables au problème d’optimisation, ce qui permet au solveur de décider automatiquement de la zone d’intersection entre deux polygones en contact ou encore de décider du lieu de contact sur une surface non plane.Nous présentons une reformulation du PG qui gêre nativement les variétés non Euclidiennes et nous permet de formuler des problèmes mathématiques plus élégants et efficaces. Pour résoudre de tels problèmes, nous avons developpé un solveur non linéaire par SQP quisupporte nativement les variables sur variétés. Ainsi, nous avons une meilleure maîtrise de notre solveur et pouvons le spécialiser pour la résolution de problèmes de robotique

Génération de Posture Multi-Contact Viable pour Robot Humanoïde par Optimisation non-linéaire sur Variétés

Humanoid robots are complex poly-articulated structures whose kinematics and dynamics are governed by nonlinear equations. Finding viable postures to realize set-point task objectives under a set of constraints (intrinsic and extrinsic limitations) is a key issue in the planning of robot motion and an important feature of any robotics framework. It is handled by the so called posture generator (PG) that consists in formalizing the viable posture as the solution to a nonlinear optimization problem. We present several extensions to the state-of-the-art by exploring new formulations and resolution methods for the posture generation problems. We reformulate the notion of contact constraints by adding variables to enrich our optimization problem and allow the solver to decide on the shape of the intersection of contact polygons or of the location of a contact point on a non-flat surface. We present a reformulation of the PG problem that encompasses non-Euclidean manifolds natively for a more elegant and efficient mathematical formulation of the problems. To solve such problems, we decided to implement a new SQP solver that is most suited to non-Euclidean manifolds structural objects. By doing so, we have a better mastering in the way to tune and specialize our solver for robotics problems.Un robot humanoïde est un système polyarticulé complexe dont la cinématique et la dynamique sont gouvernées par des équations non linéaires. Trouver des postures viables qui minimisent une tâche objectif tout en satisfaisant un ensemble de contraintes (intrinsèques ou extrinsèques) est un problème central pour la planification de mouvement robotique et est une fonctionnalité importante de tout logiciel de robotique. Le générateur de posture (PG) a pour rôle de trouver une posture viable en formulant puis résolvant un problème d’optimisation non linéaire. Nous étendons l’état de l’art en proposant de nouvelles formulations et méthodes de résolution de problèmes de génération de postures. Nous enrichissons la formulation de contraintes de contact par ajout de variables au problème d’optimisation, ce qui permet au solveur de décider automatiquement de la zone d’intersection entre deux polygones en contact ou encore de décider du lieu de contact sur une surface non plane. Nous présentons une reformulation du PG qui gère nativement les variétés non Euclidiennes et nous permet de formuler des problèmes mathématiques plus élégants et efficaces. Pour résoudre de tels problèmes, nous avons développé un solveur non linéaire par SQP qui supporte nativement les variables sur variétés. Ainsi, nous avons une meilleure maîtrise de notre solveur et pouvons le spécialiser pour la résolution de problèmes de robotique

Collision avoidance based on separating planes for feet trajectory generation

International audienceIn this paper, we present a formulation of the collision avoidance constraints that relies on the use of separating planes instead of a distance function. This formulation has the advantage of being defined and continuously differentiable in every situation. Because it introduces additional variables to the optimization problems, making it bigger and potentially slowing down its resolution, we propose a different resolution method that takes advantage of the independence of the variables, to form two subproblems that can be solved efficiently in an alternate problem fashion. We present some preliminary results using this approach in order to highlight its potential and promises in terms of convergence speed and robustness