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

2025-02-10

AI Summary

This work addresses reward-driven trajectory planning for autonomous robots navigating a predefined set of waypoints under multiple constraints: obstacle avoidance, dynamical feasibility (state/input and their derivatives), task time windows, and maximum travel distance. The problem is formulated as a coupled optimization of a Generalized Prize-Collecting Traveling Salesman Problem (GPCTSP) and real-time trajectory generation. To solve it, we propose a novel genetic algorithm incorporating three key innovations: (i) Dynamic Time Warping–based crossover for robust path sequence evolution; (ii) Extended convex combination projection for constraint-satisfying trajectory initialization; and (iii) a differential-flatness- and clothoid-based penalty mechanism for infeasible trajectories. Evaluated on ground vehicles, quadrotors, and quadrupedal robots, our method significantly outperforms minimum-snap/jerk polynomial baselines—achieving higher cumulative reward by prioritizing high-value waypoints while strictly satisfying all constraints, and maintaining real-time performance and trajectory feasibility.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper introduces a new mission planning algorithm for autonomous robots that enables the reward-based selection of an optimal waypoint sequence from a predefined set. The algorithm computes a feasible trajectory and corresponding control inputs for a robot to navigate between waypoints while avoiding obstacles, maximizing the total reward, and adhering to constraints on state, input and its derivatives, mission time window, and maximum distance. This also solves a generalized prize-collecting traveling salesman problem. The proposed algorithm employs a new genetic algorithm that evolves solution candidates toward the optimal solution based on a fitness function and crossover. During fitness evaluation, a penalty method enforces constraints, and the differential flatness property with clothoid curves efficiently penalizes infeasible trajectories. The Euler spiral method showed promising results for trajectory parameterization compared to minimum snap and jerk polynomials. Due to the discrete exploration space, crossover is performed using a dynamic time-warping-based method and extended convex combination with projection. A mutation step enhances exploration. Results demonstrate the algorithm's ability to find the optimal waypoint sequence, fulfill constraints, avoid infeasible waypoints, and prioritize high-reward ones. Simulations and experiments with a ground vehicle, quadrotor, and quadruped are presented, complemented by benchmarking and a time-complexity analysis.

Problem

• Reward-based trajectory planning for autonomous robots.
• Obstacle avoidance and optimal waypoint sequence selection.
• Genetic algorithm for solving prize-collecting TSP.

Innovation

• Reward-based genetic algorithm
• Clothoid curves for trajectories
• Dynamic time-warping crossover