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, 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 experiments with a ground vehicle, quadrotor, and quadruped, supported by benchmarking and time-complexity analysis. Note to Practitioners—This work addresses the challenge of managing multiple tasks within limited resources in cyber-physical systems, where tasks vary in priority and maximizing total reward is critical. We propose an evolutionary-inspired algorithm that optimizes task selection and prioritization in a motion planning context, generating trajectories that respect robot capabilities while favoring higher-priority tasks and potentially bypassing lower-priority ones to fulfill constraints. The algorithm integrates with traditional motion planning techniques, ensuring safe, resource-aware trajectories. It has been validated on a ground vehicle, a quadruped robot, and a quadrotor drone, demonstrating adaptability across platforms with varying constraints. Practical contributions include the flexibility of the method to accommodate different resource limitations, such as time, distance, and energy. The current formulation assumes static rewards and constraints; future work will explore real-time adaptation and extensions to broader classes of robots, including collaborative scenarios involving human-robot interaction.