A Riemannian Metric Design for Smooth and Energy-efficient Trajectory Generation of 1-DoF Port-Hamiltonian Systems

This paper proposes a procedure to design a Rie-mannian metric to generate a smooth and energy-efficient input trajectory for Hamiltonian systems with one degree of freedom. Introducing a Riemannian metric into a phase space enables us to measure lengths of solution trajectories. By analyzing Hamil-tonian (energy) structures, a metric corresponding to energy efficiency can be designed. Then an optimal control problem using the designed metric is formulated. The obtained objective function is given as a quadratic form, so the smoothness of input trajectories is guaranteed while their shape is similar to ones of Ll optimal control.