Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911170120646656 |
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| author | Ratheesh, Akash Pacelli, Vincent Saravanos, Augustinos D. Theodorou, Evangelos A. |
| author_facet | Ratheesh, Akash Pacelli, Vincent Saravanos, Augustinos D. Theodorou, Evangelos A. |
| contents | This paper presents a novel algorithm for solving distribution steering problems featuring nonlinear dynamics and chance constraints. Covariance steering (CS) is an emerging methodology in stochastic optimal control that poses constraints on the first two moments of the state distribution -- thereby being more tractable than full distributional control. Nevertheless, a significant limitation of current approaches for solving nonlinear CS problems, such as sequential convex programming (SCP), is that they often generate infeasible or poor results due to the large number of constraints. In this paper, we address these challenges, by proposing an operator splitting CS approach that temporarily decouples the full problem into subproblems that can be solved in parallel. This relaxation does not require intermediate iterates to satisfy all constraints simultaneously prior to convergence, which enhances exploration and improves feasibility in such non-convex settings. Simulation results across a variety of robotics applications verify the ability of the proposed method to find better solutions even under stricter safety constraints than standard SCP. Finally, the applicability of our framework on real systems is also confirmed through hardware demonstrations |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11211 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control Ratheesh, Akash Pacelli, Vincent Saravanos, Augustinos D. Theodorou, Evangelos A. Robotics Optimization and Control This paper presents a novel algorithm for solving distribution steering problems featuring nonlinear dynamics and chance constraints. Covariance steering (CS) is an emerging methodology in stochastic optimal control that poses constraints on the first two moments of the state distribution -- thereby being more tractable than full distributional control. Nevertheless, a significant limitation of current approaches for solving nonlinear CS problems, such as sequential convex programming (SCP), is that they often generate infeasible or poor results due to the large number of constraints. In this paper, we address these challenges, by proposing an operator splitting CS approach that temporarily decouples the full problem into subproblems that can be solved in parallel. This relaxation does not require intermediate iterates to satisfy all constraints simultaneously prior to convergence, which enhances exploration and improves feasibility in such non-convex settings. Simulation results across a variety of robotics applications verify the ability of the proposed method to find better solutions even under stricter safety constraints than standard SCP. Finally, the applicability of our framework on real systems is also confirmed through hardware demonstrations |
| title | Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control |
| topic | Robotics Optimization and Control |
| url | https://arxiv.org/abs/2411.11211 |