On-Line Feasible Wrench Polytope Evaluation Based on Human Musculoskeletal Models: An Iterative Convex Hull Method

Abstract

Many recent human-robot collaboration strategies, such as Assist-As-Needed (AAN), are promoting humancentered robot control, where the robot continuously adapts its assistance level based on the real-time need of its human counterpart. One of the fundamental assumptions of these approaches is the ability to measure or estimate the physical capacity of humans in real-time.In this work, we propose an algorithm for the feasibility set analysis of a generic class of linear algebra problems. This novel iterative convex-hull method is applied to the determination of the feasible cartesian wrench polytope associated to a musculoskeletal model of the human upper limb. The method is capable of running in real-time and allows the user to define the desired estimation accuracy. The algorithm performance analysis shows that the execution time has near-linear relationship to the considered number of muscles, as opposed to the exponential relationship of the conventional methods. Finally, real-time robot control application of the algorithm is demonstrated in a Collaborative carrying experiment, where a human operator and a Franka Emika Panda robot jointly carry a 7kg object. The robot is controlled in accordance to the AAN paradigm maintaining the load carried by the human operator at 30% of its carrying capacity.

Derivative-Free Optimization Approaches for Force Polytopes Prediction

“…All scripts are written in Python 3.8 and the packages biorbd, pycapacity 1.2.19 and ZOOpt 0.3.0 have been used to describe the musculoskeletal model, the ICH method and the SRACOS implementation. The ICH method is set to a tolerance of 1N [1]. All algorithms stop after exploring 32000 solutions.…”

“…Enumerating the vertices of P is impractical, due to the high combinatorics involved in the zonotope computation [2]. The Iterative Convex Hull (ICH) method allows a reasonably fast approximation of the vertices within a chosen tolerance [1]. Using a 2x8-cores (2.61GHz) Intel i9-11950H processor, the ICH (with a tolerance of 1N) mean time for 100 randomly generated 3D affine subspaces and 7D zonotopes built from 50D hypercubes is 1.03 ± 0.05 seconds.…”

“…It sees application in physical Human-Robot Interaction (pHRI), in which an interaction between the operator's hand and the robot's end-effector is considered. Knowing the operator's force capacities allows the robot to adjust its assistance to avoid exceeding force limits [1]. However, these limits depend on the operator's posture, muscle geometry and biomechanical properties.…”

Approximating Robot Reachable Space Using Convex Polytopes

“…In order to avoid enumerating all the vertices of the high-dimensional joint torque polytope P τ , as the most complex operation of this polytope enumeration, Iterative convex hull method [10] (ICHM) is used, allowing to directly enumerate low-dimensional cartesian polytope P x . This iterative method is based on successively applying Linear programming (LP) and Convex-Hull (CH) algorithms and is able to find both vertex and half-space representation of this polytope at the same time.…”

Comparison of strength profile representations using musculoskeletal models and their applications in robotics

“…Additionally, musculoskeletal models also consider multi-articular muscles, agonist-antagonist co-contraction, and other biomechanical factors that affect whole-limb strength. Several methods have been developed to utilize musculoskeletal models for estimating the strength at the end of a human limb, with different approaches to calculating and representing this strength being proposed ( Carmichael and Liu, 2013 ; Hernandez et al, 2018 ; Petrič et al, 2019 ; Sohn et al, 2019 ; Skuric et al, 2022 ). Figure 1 shows three methods commonly used for strength representation at the hand.…”