• Rural Digital Europe
• 2012-2021close
• HAL-Pasteur close

Author summary Humans are talented at coordinating movements with one another through a multitude of objects such as a hard table or a soft mattress. Depending on the softness of the object, the force we perceive from the partner can be strong enough to sense directional cues, or could be too weak to understand the partner’s movement intention. How do we coordinate physical movements governed by such differing mechanics? Our task is inspired by a pair moving through a dancefloor during Tango dancing; we tested subjects in pairs who jointly chased a moving target with their right hands, which were banded together by either a strong, medium or weak elastic band. By measuring the change in each partner’s performance at the task, and the muscular effort they exerted, we characterized the changes in each partner’s behavior as a function of the strength of the elastic band that coupled them together. By employing a computational simulation of the task, we tested different coordination mechanisms to see what explained the data best. We found that, regardless of the coupling strength, each subject infers the movement intention of their partner, but this process deteriorates with softer coupling. To move a hard table together, humans may coordinate by following the dominant partner’s motion [1–4], but this strategy is unsuitable for a soft mattress where the perceived forces are small. How do partners readily coordinate in such differing interaction dynamics? To address this, we investigated how pairs tracked a target using flexion-extension of their wrists, which were coupled by a hard, medium or soft virtual elastic band. Tracking performance monotonically increased with a stiffer band for the worse partner, who had higher tracking error, at the cost of the skilled partner’s muscular effort. This suggests that the worse partner followed the skilled one’s lead, but simulations show that the results are better explained by a model where partners share movement goals through the forces, whilst the coupling dynamics determine the capacity of communicable information. This model elucidates the versatile mechanism by which humans can coordinate during both hard and soft physical interactions to ensure maximum performance with minimal effort.

Rigid body dynamics is a well-established framework in robotics. It can be used to expose the analytic form of kinematic and dynamic functions of the robot model. So far, two major algorithms, namely the recursive Newton-Euler algorithm (RNEA) and the articulated body algorithm (ABA), have been proposed to compute the inverse dynamics and the forward dynamics in a few microseconds. Evaluating their derivatives is an important challenge for various robotic applications (optimal control, estimation, co-design or reinforcement learning). However it remains time consuming, whether using finite differences or automatic differentiation. In this paper, we propose new algorithms to efficiently compute them thanks to closed-form formulations. Using the chain rule and adequate algebraic differentiation of spatial algebra, we firstly differentiate explicitly RNEA. Then, using properties about the derivative of function composition, we show that the same algorithm can also be used to compute the derivatives of ABA with a marginal additional cost. For this purpose, we introduce a new algorithm to compute the inverse of the joint-space inertia matrix, without explicitly computing the matrix itself. All the algorithms are implemented in our open-source C++ framework called Pinocchio. Benchmarks show computational costs varying between 3 microseconds (for a 7-dof arm) up to 17 microseconds (for a 36-dof humanoid), outperforming the alternative approaches of the state of the art. International audience