Physical feasibility of robot base inertial parameter identification: A linear matrix inequality approach

Identification of robot dynamics is a key issue in boosting the performance of model-based control techniques, having also a key role in realistic simulation. Robot dynamic parameters have physical meaning, hence parameter estimations must correspond to physically feasible values. Since it is only possible to identify linear combinations of parameters (the base parameters) the physical feasibility of such combinations cannot be directly asserted. In this paper we show that feasibility conditions define a convex set and can be written as a linear matrix inequality (LMI), suitable for semidefinite programming (SDP) techniques. We propose three methods based on LMI-SDP to deal with the feasibility of base parameters. The first method checks if a given base parameter estimation has physical meaning. The second method corrects infeasible estimations, finding the closest feasible base parameters. These two methods can be applied to existing regression techniques. The third method performs parameter identification through ordinary least squares regression constrained to the feasible space, guaranteeing the optimal solution. Experiments with a seven-link robot manipulator are provided, and efficiency and scalability are discussed.