Overview : This project develops an energy-optimal motion planning algorithm for a unicycle robot performing point-to-point maneuvers in environments with static obstacles. By redefining the kinematic model in the geometric center space, the formulation is simplified using a reduced-order representation. The approach combines two stages: pre-planning and re-planning. In the pre-planning stage, an obstacle-free optimal control problem is solved, and a perturbation-based controller integrates nominal feedforward control with feedback tracking. In the re-planning stage, control barrier functions enforce safety constraints through point-wise optimization, providing minimum intervention control around obstacles. Safety metrics trigger re-planning only when necessary, resulting in near-optimal trajectories that balance efficiency and collision avoidance.

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