The key highlights and insights of this work are:
The authors represent the robot's geometry as a semialgebraic set defined by polynomial inequalities, which allows for the characterization of robots with general shapes.
To address robot navigation in obstacle-dense environments, the authors exploit the free space directly to construct a sequence of free regions and allocate each waypoint on the trajectory to a specific region.
The authors formulate a Sums-of-Squares (SOS) optimization problem to render the containment relationship between the robot and the free space computationally tractable. This SOS optimization problem is further reformulated as a semidefinite program (SDP).
The authors derive the analytical solution to the gradient of the minimum scaling factor with respect to the robot configuration, which facilitates the use of gradient-based methods in efficiently solving the trajectory optimization problem.
Through simulations and real-world experiments, the proposed trajectory optimization approach is validated in various challenging scenarios, demonstrating its effectiveness in generating collision-free trajectories in dense and intricate environments populated with obstacles.
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by Yulin Li,Chu... at arxiv.org 04-09-2024
https://arxiv.org/pdf/2404.05242.pdfDeeper Inquiries