Motion Optimization for Musculoskeletal Dynamics: A Flatness-Based Polynomial Approach

TL;DR

This paper introduces a novel polynomial-based flatness approach for efficient trajectory optimization in musculoskeletal models, combining neural control, muscle dynamics, and sum-of-squares methods to reduce computational complexity.

Contribution

It presents a new flatness-based polynomial method that simplifies musculoskeletal trajectory optimization by eliminating dynamic constraints and enabling linear programming solutions.

Findings

Reduces optimization to linear programming problems.

Demonstrates efficiency with simulation examples.

Provides recursive feasibility proof for polynomial optimization.

Abstract

A new approach for trajectory optimization of musculoskeletal dynamic models is introduced. The model combines rigid body and muscle dynamics described with a Hill-type model driven by neural control inputs. The objective is to find input and state trajectories which are optimal with respect to a minimum-effort objective and meet constraints associated with musculoskeletal models. The measure of effort is given by the integral of pairwise average forces of the agonist-antagonist muscles. The concepts of flat parameterization of nonlinear systems and sum-of-squares optimization are combined to yield a method that eliminates the numerous set of dynamic constraints present in collocation methods. With terminal equilibrium, optimization reduces to a feasible linear program, and a recursive feasibility proof is given for more general polynomial optimization cases. The methods of the paper can be used as a basis for fast and efficient solvers for hierarchical and receding-horizon control schemes. Two simulation examples are included to illustrate the proposed methods