Recursive dynamics and feedback linearizing control of serial-chain manipulators

Manipulators that have the compliance necessary to share the same workspace and safely interact with people are currently of great interest to both the industrial as well as research communities. This work focuses on the development of nonlinear controllers for compliant serial-chain manipulators. In particular, we derive a novel algorithm that analytically computes feedback linearizing controllers for N-link manipulators with compliant joints. It is possible to express the controllers in closed form because we use geometric notation to concisely derive an algorithm that analytically inverts the manipulator´s generalized inertia matrix. The resultant recursive dynamic expressions make it possible to solve for the feedback linearizing controllers exactly. Simulation results which apply the closed-form controllers to the analytic dynamics of a six-joint serial manipulator with series-elastic actuators are provided.