Use of the nonlinear observability rank condition for improved parametric estimation

The correct way to design controllers for dynamic robots is still very much an open question. This is in a large part due to the complexity and uncertainty in modeling their nonlinear dynamics. In this work, we focus on deriving concise dynamic expressions for a particular class of robots that can be used to better reduce uncertainty with respect to unknown parameters in realtime. We accomplish this by using an extended Kalman filtering framework in conjunction with an online controller that continuously maximizes a local measure of nonlinear observability. The main novel contribution of this work is that we directly use the nonlinear observability rank condition to derive the measure of observability at each time step. We are able to make this extension in part by focusing on serial-chain systems and exploiting the geometric structure in their dynamic models. In particular, we derive concise, closed-form and exact analytical representations for the forward dynamics, linearization, and nonlinear observability rank condition of a fixed-base serial manipulator with actively controlled elastic joints. An example is presented in which the spring constants and damping coefficients for a series-elastic actuated manipulator are estimated using the online observability maximizing techniques we derive.