Sequential semidefinite optimization for physically and statistically consistent robot identification

Abstract This work considers the problem of dynamic identification for robotic mechanisms given noisy measurements of configuration variables and applied torques. Conventionally, this problem is solved via least-squares, exploiting linearity properties of the inverse dynamics model for rigid-body systems. However, the nonlinear dependency of this model on configurations and velocities gives rise to bias in the resultant estimates when using noisy or even filtered data. Further, these biases can cause parameters of best fit to be non-physical, potentially leading to an ill-posed forward dynamic model. The main contribution of this paper is to propose a sequential semidefinite optimization procedure to both (1) ensure the physical consistency of the identified model and (2) maintain the statistical consistency of the estimator. The new method validates both a direct and inverse dynamic identification model (DIDIM), and also ensures that intermediate iterates of the algorithm remain physically valid. Due to these favorable properties, the method is named a Physically-Consistent DIDIM (PC-DIDIM) approach. Recent statistical hypothesis tests for instrumental variable approaches are generalized for application with a PC-DIDIM approach. Experimental results with a six-degree-of-freedom industrial robot supported by Monte Carlo simulations show the effectiveness of the new method and robustness benefits in comparison to conventional least-squares and the vanilla DIDIM method.