  We introduce optimal energy shaping as an enhancement of classical
passivity-based control methods. A promising feature of passivity theory,
alongside stability, has traditionally been claimed to be intuitive performance
tuning along the execution of a given task. However, a systematic approach to
adjust performance within a passive control framework has yet to be developed,
as each method relies on few and problem-specific practical insights. Here, we
cast the classic energy-shaping control design process in an optimal control
framework; once a task-dependent performance metric is defined, an optimal
solution is systematically obtained through an iterative procedure relying on
neural networks and gradient-based optimization. The proposed method is
validated on state-regulation tasks.
