Canonical transformations used to derive robot control laws from a port-controlled Hamiltonian system perspective

This paper addresses the problem of deriving control laws for robot manipulators in the framework of port-controlled Hamiltonian systems via canonical transformations and passivity-based control. The control design is focused on the presentation of a new energy-shaping methodology for tracking control based on the introduction of virtual non-homogeneous fields where a desired energy is defined to compensate for the actual energy of the robot manipulator while a virtual field forces the system to track a general reference trajectory. This requires use of the Legendre-Fenchel transformation and allows for the derivation standard control laws in the robotics field such as PD control with gravity compensation or PD with precompensation. Finally, the passivity of the input-output mapping of the non-autonomous Hamiltonian system is analyzed in detail, resulting in new Lyapunov candidate functions having their roots in physics.