Reward-Based Collision-Free Algorithm for Trajectory Planning of Autonomous Robots

This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission time, and distance constraints. The formulation extends the prize-collecting traveling salesman problem. A tailored genetic algorithm evolves candidate solutions using a fitness function, crossover, and mutation, with constraint enforcement via a penalty method. Differential flatness and clothoid curves are employed to penalize infeasible trajectories efficiently, while the Euler spiral method ensures curvature-continuous trajectories with bounded curvature, enhancing dynamic feasibility and mitigating oscillations typical of minimum-jerk and snap parameterizations. Due to the discrete variable length optimization space, crossover is performed using a dynamic time-warping-based method and extended convex combination with projection. The algorithm's performance is validated through simulations and experiments with a ground vehicle, quadrotor, and quadruped, supported by benchmarking and time-complexity analysis.