Collision-Free Trajectory Optimization in Cluttered Environments with Sums-of-Squares Programming
Authors: Yulin Li, Chunxin Zheng, Kai Chen, Yusen Xie, Xindong Tang, Michael Yu Wang, Jun Ma
Summary: On this work, we suggest a trajectory optimization method for robotic navigation in cluttered 3D environments. We signify the robotic’s geometry as a semialgebraic set outlined by polynomial inequalities such that robots with basic shapes could be suitably characterised. To handle the robotic navigation process in obstacle-dense environments, we exploit the free area on to assemble a sequence of free areas, and allocate every waypoint on the trajectory to a selected area. Then, we incorporate a uniform scaling issue for every free area, and formulate a Sums-of-Squares (SOS) optimization downside that renders the containment relationship between the robotic and the free area computationally tractable. The SOS optimization downside is additional reformulated to a semidefinite program (SDP), and the collision-free constraints are proven to be equal to limiting the scaling issue alongside the complete trajectory. On this context, the robotic at a selected configuration is tailor-made to remain inside the free area. Subsequent, to unravel the trajectory optimization downside with the proposed security constraints (that are implicitly depending on the robotic configurations), we derive the analytical resolution to the gradient of the minimal scaling issue with respect to the robotic configuration. Because of this, this seamlessly facilitates using gradient-based strategies in environment friendly fixing of the trajectory optimization downside. Via a collection of simulations and real-world experiments, the proposed trajectory optimization method is validated in varied difficult situations, and the outcomes exhibit its effectiveness in producing collision-free trajectories in dense and complex environments populated with obstacles.
