6. Passivity-Based Tracking Control of a Flexible Link Robot

This contribution addresses modeling and control of highly complex nonlinear mechanical systems such as an articulated robot with two flexible links and three flexible joints. We employ the Projection Equation in subsystem formulation, a very efficient method for modeling repeating assemblies and beam elasticities and apply a Ritz expansion to obtain ordinary differential equations of motion. For model-based control design, the small elastic deformations of the beams are approximated with linear springs and dampers in a lumped element model. On this basis, a control design with two degrees of freedom is proposed: a flatness-based feed forward and a passivity-based feedback control technique of interconnection and damping assignment. Further, we deal with acceleration and angular rate measurements to compute all system states used in the feedback loop. Finally, the proposed strategies are validated by measurements from a fast straight line in space and a ball catching scenario.