Symplectic Discrete-Time Control of Flexible-Joint Robots: Experiments with Two Links

We present the application and experimental validation of discrete-time control implementation based on symplectic integration - in short referred to as symplectic discrete-time control - to a serial robot manipulator with flexible-joints. Applying the implicit midpoint rule as a simple and popular symplectic integration scheme to both the model of the sampled system and the desired target dynamics, yields a discrete-time control law with the same structure as in continuous time. The arguments are, however, predicted stage values on the subsequent sampling interval resulting from a half implicit Euler step for the target system. The approach can be easily extended to a purely position-based feedback law. The experimental validation on a lightweight robot (KUKA LWR IV+) confirms the expected improvements at low sampling rates, with an increase in the assignable closed-loop stiffness of up to 29 %.