Successive linearization based model predictive control of variable stiffness actuated robots

Variable stiffness actuation is a new design paradigm for high performance and energy efficient robots with inherent safety features. Nonlinear model predictive control (NMPC) was employed to control these robots due to its ability to cope with constrained and nonlinear systems. Even though the results for NMPC are promising, one major weakness is the computational cost of this algorithm. It restricts the use of NMPC to low degree of freedom robots with relatively slow dynamics. This problem can be alleviated by finding an approximate linear representation of the system and using less computation hungry traditional model predictive control (MPC). In this work, we present our successive linearization based MPC (SLMPC) framework for variable stiffness actuated (VSA) robots. The system is linearized and discretized at every sampling instant and a quadratic problem is formulated using this discrete-Time linear model. Solution of this quadratic problem provides the control inputs for the control horizon. In order to compare our scheme to NMPC, we conducted experiments with a reaction wheel augmented VSA system. For a 16 s trajectory tracking experiment, the root-mean-square errors were 0.54 and 0.64 degrees for NMPC and SLMPC methods, respectively, whereas the average computation time of the control rule was 2.17 ms for NMPC and 1.25 ms for SLMPC. Halving the computation time without compromising tracking performance shows the potential of our approach as a viable control alternative for VSA robots.