Symplectic integration for optimal ergodic control
Title | Symplectic integration for optimal ergodic control |
Publication Type | Conference Paper |
Year of Publication | 2015 |
Authors | Prabhakar, A., Flaßkamp, K., Murphey, T. D. |
Conference Name | 2015 54th IEEE Conference on Decision and Control (CDC) |
Date Published | dec |
Keywords | autonomous 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. |
DOI | 10.1109/CDC.2015.7402607 |
Citation Key | prabhakar_symplectic_2015 |
- nonlinear dynamics
- trajectory optimization
- trajectory control
- time-averaged trajectory
- symplectic integration
- statistical representation
- statistical analysis
- standard first-order discretization techniques
- spatial distribution
- search algorithm
- pubcrawl170110
- Path Planning
- optimal search trajectory
- optimal ergodic control
- optimal control
- autonomous active exploration
- nonlinear control systems
- mobile robots
- Measurement
- Linear programming
- iterative optimal control algorithm
- Iterative methods
- Heuristic algorithms
- graphical models
- Distribution functions
- discrete-time iterative trajectory optimization approach
- discrete time systems
- continuous-time trajectory optimization algorithm
- continuous time systems