Impedance controllers are widely used to stabilize feedback systems. Although simple to deploy, these linear controllers are often not optimized for the task at hand. Therefore, a generalized nonlinear feedback law defined as the gradient of the potential and dissipation maps is presented. An optimal control framework is built around the idea that solving a large number of optimal control problems for the same feedback maps will make them optimal for a specific task. The maps can be adapted to a specific scenario by changing the desired task, constraints and objective functions.
2 case studies for 1-DoF positioning tasks are explored, and the resulting maps are analyzed.