Spline Trajectory Tracking and Obstacle Avoidance for Mobile Agents via Convex Optimization
CoRR(2024)
摘要
We propose an output feedback control-based motion planning technique for
agents to enable them to converge to a specified polynomial trajectory while
imposing a set of safety constraints on our controller to avoid collisions
within the free configuration space (polygonal environment). To achieve this,
we 1) decompose our polygonal environment into different overlapping cells 2)
write out our polynomial trajectories as the output of a reference dynamical
system with given initial conditions 3) formulate convergence and safety
constraints as Linear Matrix Inequalities (LMIs) on our controller using
Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) and 4)
solve a semi-definite programming (SDP) problem with convergence and safety
constraints imposed to synthesize a controller for each convex cell. Extensive
simulations are included to test our motion planning method under different
initial conditions and different reference trajectories. The synthesized
controller is robust to changes in initial conditions and is always safe
relative to the boundaries of the polygonal environment.
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