Geometry-aware manipulability learning, tracking, and transfer

Abstract

Body posture influences human and robot performance in manipulation tasks, as appropriate poses facilitate motion or the exertion of force along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control, and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or applying a specific force. In this context, this article presents a novel manipulability transfer framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive-definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.

Learning from demonstration using products of experts: Applications to manipulation and task prioritization

“…A Wishart distribution is not expressive enough to define variances along different directions. In Jaquier et al (2021), it is proposed to use Gaussian distributions in the tangent space of manifolds. This choice is motivated by the geometry of symmetric positive-definite matrices (SPD).…”

“…Similarly, such consideration is important to transfer manipulability objectives between robots with different kinematic chains. In Jaquier et al (2021), manipulability ellipsoid distributions are expressed on the set of SPD. We show in the experiments of Section 6.2 that manipulability-related tasks would be better transferred by considering that the distributions are expressed on subsets of these matrices.…”

Analysis and Transfer of Human Movement Manipulability in Industry-like Activities

“…The Riemannian manifold framework is also exploited for human-robot manipulability transfer in Section IV. As shown in [16], a geometry-aware approach proves to be crucial for transferring manipulability requirements to robots in terms of accuracy, stability and convergence, beyond providing an appropriate mathematical treatment of the problem.…”

“…Namely, we propose to transfer the manipulability requirements of screwing and carrying tasks (SM and C5) from a human to a Centauro robot [20]. To do so, we exploit the manipulability transfer framework introduced in [21], [16], that allows robots to learn and reproduce manipulability ellipsoids from human demonstrations. For both tasks, the demonstrations consist of the 15 recorded trials of the participant 541, previously used for the manipulability analysis.…”

“…The controllers details can be found in [16]. Figure 6a shows the evolution of the posture and the manipulability of Centauro during the reproduction of the pre-screwing motion with its right arm.…”