Automatic identification of dynamic piecewise affine models for a running robot

This paper presents a simple, data-driven technique for identifying models for the dynamics of legged robots. Piecewise Affine (PWA) models are used to approximate the observed nonlinear system dynamics of a hexapedal millirobot. The high dimension of the state space (16) and very large number of state observations (~100,000) motivated the use of statistical clustering methods to automatically choose the submodel regions. Comparisons of models with 1 to 50 PWA regions are analyzed with respect to state derivative prediction and forward simulation accuracy. Derivative prediction accuracy was shown to reduce average in-axis absolute error by up to 52% compared to a null estimator. Simulation results show tracking of state trajectories over one stride length, and the degradation of simulation prediction is analyzed across model complexity and time horizon. We describe metrics for comparing the performance of different model complexities across one-step and simulation predictions.