Abstract
This paper investigates optimization-based planning methods for generating trajectories which are robust to state uncertainty in undersensed and underactuated systems. Specifically, these methods are applied to an undersensed robotic hill climbing system. In previous work, divergence metrics based on contraction analysis were used to quantify robustness of a trajectory to state uncertainty in conjunction with a kinodynamic RRT planner to guide the planner towards more convergent directions. Resulting trajectories were sub-optimal or needed to be smoothed prior to implementation. This work proposes an optimization framework to plan optimally robust and smooth trajectories which can also be readily implemented on the robotic hill climbing problem. A new hill climbing controller is also presented which can guarantee for the first time the strongest result of contraction analysis, global asymptotic convergence, where possible. Trajectories created using the new trajectory optimization framework and hill controller are shown to be smoother and more robust than previous methods as well as an asymptotically optimal versions of previous methods.
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Acknowledgment
Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-19-1-0080. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
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Kong, N.J., Johnson, A.M. (2022). Optimally Convergent Trajectories for Navigation. In: Asfour, T., Yoshida, E., Park, J., Christensen, H., Khatib, O. (eds) Robotics Research. ISRR 2019. Springer Proceedings in Advanced Robotics, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-030-95459-8_5
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DOI: https://doi.org/10.1007/978-3-030-95459-8_5
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