Quasi-Static Mechanical Manipulation as an Optimal Process

This work focuses on quasi-static manipulation of elastically-interconnected rigid bodies by an agent, e.g. a robot assembling mechanical parts. The whole system is seen as an underactuated control problem, where only certain degrees of freedom (e.g. robot end-effector) are directly controllable. Mechanical contact is regularized via nonlinear yet smooth elastic interaction giving rise to a smooth total potential energy. The squared-Hessian of such a potential is used as optimality measure and quasi-static mechanical manipulation is rephrased as optimal path planning on the manifold of mechanical equilibria. A simple example of an elastically-driven inverted pendulum is presented as a toy model. Numerical implementation as a minimum path on graphs is also described.