Visible to the public Symplectic integration for optimal ergodic control

TitleSymplectic integration for optimal ergodic control
Publication TypeConference Paper
Year of Publication2015
AuthorsPrabhakar, A., Flaßkamp, K., Murphey, T. D.
Conference Name2015 54th IEEE Conference on Decision and Control (CDC)
Date Publisheddec
Keywordsautonomous active exploration, continuous time systems, continuous-time trajectory optimization algorithm, discrete time systems, discrete-time iterative trajectory optimization approach, Distribution functions, graphical models, Heuristic algorithms, Iterative methods, iterative optimal control algorithm, Linear programming, Measurement, mobile robots, nonlinear control systems, nonlinear dynamics, optimal control, optimal ergodic control, optimal search trajectory, path planning, pubcrawl170110, search algorithm, spatial distribution, standard first-order discretization techniques, statistical analysis, statistical representation, symplectic integration, time-averaged trajectory, trajectory control, trajectory optimization
Abstract

Autonomous active exploration requires search algorithms that can effectively balance the need for workspace coverage with energetic costs. We present a strategy for planning optimal search trajectories with respect to the distribution of expected information over a workspace. We formulate an iterative optimal control algorithm for general nonlinear dynamics, where the metric for information gain is the difference between the spatial distribution and the statistical representation of the time-averaged trajectory, i.e. ergodicity. Previous work has designed a continuous-time trajectory optimization algorithm. In this paper, we derive two discrete-time iterative trajectory optimization approaches, one based on standard first-order discretization and the other using symplectic integration. The discrete-time methods based on first-order discretization techniques are both faster than the continuous-time method in the studied examples. Moreover, we show that even for a simple system, the choice of discretization has a dramatic impact on the resulting control and state trajectories. While the standard discretization method turns unstable, the symplectic method, which is structure-preserving, achieves lower values for the objective.

DOI10.1109/CDC.2015.7402607
Citation Keyprabhakar_symplectic_2015