A Novel Passivity-Based Trajectory Tracking Control For Conservative Mechanical Systems

TL;DR

This paper introduces a passivity-based energy shaping control method for conservative mechanical systems that enables asymptotic tracking of non-stationary trajectories by shaping the system's energy landscape.

Contribution

It develops a novel Hamiltonian modeling approach for reference trajectories and integrates energy shaping with a virtual spring-damper interconnection for improved trajectory tracking.

Findings

Achieves asymptotic tracking of non-stationary trajectories.

Ensures stability through energy level regulation.

Extends passivity-based control to non-stationary trajectories.

Abstract

Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the reference trajectory and solving along the constrained trajectory to obtain a reference potential. This potential is then used as the model to shape the energy of the true system such that its free solutions include the desired reference trajectory. The proposed trajectory tracking algorithm interconnects the reference and true systems through a virtual spring damper along with an outer-loop energy pump/damper that stabilises the desired energy level of the interconnected system, ensuring asymptotic tracking of the desired trajectory. The resulting algorithm is a fully energy based trajectory tracking control for non-stationary trajectories of conservative mechanical systems.