Maximizing Fisher information using discrete mechanics and projection-based trajectory optimization

Abstract—This paper reformulates an optimization algo-rithm previously presented in continuous-time to one using structured integration and structured linearization methods from discrete mechanics. The objective is to synthesize trajecto-ries for dynamic robotic systems that improve the estimation of model parameters by using a metric on Fisher information in a nonlinear projection-based trajectory optimization algorithm. A simulation of a robot with a suspended double pendulum is used as an example system to illustrate the algorithm. Results from the simulation show that the change to a discrete mechanics formulation reduces the computation time by a factor of 19 when compared to the continuous algorithm while maintaining the same two orders of magnitude improvement in the Fisher information from the continuous-time formulation. Through the Cramer-Rao bound, the improvement in the Fisher information results in a maximum expected error reduction of the parameter estimates by up to a factor of 102. I