Abstract
Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.
Keywords
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- 1.
In this situation, indirect approaches can be used as well, cf. e.g. [61].
- 2.
See e.g. D* code for planning with primitives provided by Marin Kobilarov, Autonomous Systems, Control and Optimization (ASCO) Laboratory, Johns Hopkins University at https://github.com/jhu-asco/dsl.
- 3.
The reason for specifying the target as a circular area is that this way, the parameter dimension can be further reduced by one, as we will see below.
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Acknowledgments
We would like to acknowledge Michael Dellnitz, who has been an inspiration to us from our initial PhD time until today in many areas of research that jointly resulted in works on multiobjective optimization, dynamical systems, optimal control and symmetries.
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Flaßkamp, K., Ober-Blöbaum, S., Peitz, S. (2020). Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In: Junge, O., Schütze, O., Froyland, G., Ober-Blöbaum, S., Padberg-Gehle, K. (eds) Advances in Dynamics, Optimization and Computation. SON 2020. Studies in Systems, Decision and Control, vol 304. Springer, Cham. https://doi.org/10.1007/978-3-030-51264-4_9
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