TY - GEN
T1 - Symplectic integration for optimal ergodic control
AU - Prabhakar, Ahalya
AU - Flasskamp, Kathrin
AU - Murphey, Todd D.
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant CMMI 1334609. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC.2015.7402607
DO - 10.1109/CDC.2015.7402607
M3 - Conference contribution
AN - SCOPUS:84962010022
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2594
EP - 2600
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
Y2 - 15 December 2015 through 18 December 2015
ER -