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

This paper reformulates an optimization algorithm previously presented in continuous-time to one using structured integration and structured linearization methods from discrete mechanics. The objective is to synthesize trajectories 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.