Simulation-based LQR-trees with input and state constraints
We present an algorithm that probabilistically covers a bounded region of the state space of a nonlinear system with a sparse tree of feedback stabilized trajectories leading to a goal state. The generated tree serves as a lookup table control policy to get any reachable initial condition within tha...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73535 https://orcid.org/0000-0002-8712-7092 |
| _version_ | 1826202900166082560 |
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| author | Tedrake, Russell Louis |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Tedrake, Russell Louis |
| author_sort | Tedrake, Russell Louis |
| collection | MIT |
| description | We present an algorithm that probabilistically covers a bounded region of the state space of a nonlinear system with a sparse tree of feedback stabilized trajectories leading to a goal state. The generated tree serves as a lookup table control policy to get any reachable initial condition within that region to the goal. The approach combines motion planning with reasoning about the set of states around a trajectory for which the feedback policy of the trajectory is able to stabilize the system. The key idea is to use a random sample from the bounded region for both motion planning and approximation of the stabilizable sets by falsification; this keeps the number of samples and simulations needed to generate covering policies reasonably low. We simulate the nonlinear system to falsify the stabilizable sets, which allows enforcing input and state constraints. Compared to the algebraic verification using sums of squares optimization in our previous work, the simulation-based approximation of the stabilizable set is less exact, but considerably easier to implement and can be applied to a broader range of nonlinear systems. We show simulation results obtained with model systems and study the performance and robustness of the generated policies. |
| first_indexed | 2024-09-23T12:24:09Z |
| format | Article |
| id | mit-1721.1/73535 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:24:09Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/735352022-09-28T07:56:41Z Simulation-based LQR-trees with input and state constraints Tedrake, Russell Louis Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Tedrake, Russell Louis We present an algorithm that probabilistically covers a bounded region of the state space of a nonlinear system with a sparse tree of feedback stabilized trajectories leading to a goal state. The generated tree serves as a lookup table control policy to get any reachable initial condition within that region to the goal. The approach combines motion planning with reasoning about the set of states around a trajectory for which the feedback policy of the trajectory is able to stabilize the system. The key idea is to use a random sample from the bounded region for both motion planning and approximation of the stabilizable sets by falsification; this keeps the number of samples and simulations needed to generate covering policies reasonably low. We simulate the nonlinear system to falsify the stabilizable sets, which allows enforcing input and state constraints. Compared to the algebraic verification using sums of squares optimization in our previous work, the simulation-based approximation of the stabilizable set is less exact, but considerably easier to implement and can be applied to a broader range of nonlinear systems. We show simulation results obtained with model systems and study the performance and robustness of the generated policies. 2012-10-02T13:11:38Z 2012-10-02T13:11:38Z 2010-07 2010-05 Article http://purl.org/eprint/type/ConferencePaper 978-1-4244-5040-4 978-1-4244-5038-1 1050-4729 http://hdl.handle.net/1721.1/73535 Reist, Philipp, and Russ Tedrake. “Simulation-based LQR-trees with Input and State Constraints.” IEEE International Conference on Robotics and Automation (ICRA), 2010. 5504–5510. https://orcid.org/0000-0002-8712-7092 en_US http://dx.doi.org/10.1109/ROBOT.2010.5509893 Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2010 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers (IEEE) IEEE |
| spellingShingle | Tedrake, Russell Louis Simulation-based LQR-trees with input and state constraints |
| title | Simulation-based LQR-trees with input and state constraints |
| title_full | Simulation-based LQR-trees with input and state constraints |
| title_fullStr | Simulation-based LQR-trees with input and state constraints |
| title_full_unstemmed | Simulation-based LQR-trees with input and state constraints |
| title_short | Simulation-based LQR-trees with input and state constraints |
| title_sort | simulation based lqr trees with input and state constraints |
| url | http://hdl.handle.net/1721.1/73535 https://orcid.org/0000-0002-8712-7092 |
| work_keys_str_mv | AT tedrakerusselllouis simulationbasedlqrtreeswithinputandstateconstraints |