Learning Barrier-Certified Polynomial Dynamical Systems for Obstacle Avoidance with Robots
arxiv(2024)
摘要
Established techniques that enable robots to learn from demonstrations are
based on learning a stable dynamical system (DS). To increase the robots'
resilience to perturbations during tasks that involve static obstacle
avoidance, we propose incorporating barrier certificates into an optimization
problem to learn a stable and barrier-certified DS. Such optimization problem
can be very complex or extremely conservative when the traditional linear
parameter-varying formulation is used. Thus, different from previous approaches
in the literature, we propose to use polynomial representations for DSs, which
yields an optimization problem that can be tackled by sum-of-squares
techniques. Finally, our approach can handle obstacle shapes that fall outside
the scope of assumptions typically found in the literature concerning obstacle
avoidance within the DS learning framework. Supplementary material can be found
at the project webpage: https://martinschonger.github.io/abc-ds
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