An energy-based numerical continuation approach for quasi-static mechanical manipulation

Abstract

Robotic manipulation inherently involves contact with objects for task accomplishment. Traditional motion planning techniques, while having shown their success in collision-free scenarios, may not handle manipulation tasks effectively because they typically avoid contact. Although geometric constraints have been introduced into classical motion planners for tasks that involve interactions, they still lack the capability to fully incorporate contact. In addition, these planning methods generally do not operate on objects that cannot be directly controlled. In this work, building on a recently proposed framework for energy-based quasi-static manipulation, we propose an approach to manipulation planning by adapting a numerical continuation algorithm to compute the equilibrium manifold (EM), which is implicitly derived from physical laws. By defining a manipulation potential energy function that captures interaction and natural potentials, the numerical continuation approach is integrated with adaptive ordinary differential equations that converge to the EM. This allows discretizing the implicit manifold as a graph with a finite set of equilibria as nodes interconnected by weighted edges defined via a haptic metric. The proposed framework is evaluated with an inverted pendulum task, where the explored branch of the manifold demonstrates effectiveness.