[Paper Review] Finding Near-optimal Solutions in Multi-robot Path Planning

Michal Čáp, Peter Novák+1 more|arXiv (Cornell University)|Oct 20, 2014

Robotic Path Planning Algorithms3 references3 citations

TL;DR

This paper proposes a k-step penalty method (kPM) for multi-robot path planning that iteratively penalizes trajectory conflicts and replans individual robot paths to achieve collision-free, near-optimal solutions. Starting from individually optimal trajectories, it gradually increases penalties for proximity to other robots' paths, enabling convergence to high-quality, low-cost trajectories that outperform prioritized planning and ORCA by 4–10% and up to 40% respectively in cost.

ABSTRACT

We deal with the problem of planning collision-free trajectories for robots operating in a shared space. Given the start and destination position for each of the robots, the task is to find trajectories for all robots that reach their destinations with minimum total cost such that the robots will not collide when following the found trajectories. Our approach starts from individually optimal trajectory for each robot, which are then penalized for being in collision with other robots. The penalty is gradually increased and the individual trajectories are iteratively replanned to account for the increased penalty until a collision-free solution is found. Using extensive experimental evaluation, we find that such a penalty method constructs trajectories with near-optimal cost on the instances where the optimum is known and otherwise with 4-10 % lower cost than the trajectories generated by prioritized planning and up to 40 % cheaper than trajectories generated by local collision avoidance techniques, such as ORCA.

Motivation & Objective

• To address the challenge of finding collision-free, low-cost trajectories for multiple robots in shared environments.
• To improve upon the suboptimality and instability of prioritized planning and reactive methods like ORCA.
• To develop a scalable, iterative penalty-based method that converges toward near-optimal solutions without exponential complexity.
• To evaluate the method on synthetic and real-world environments, demonstrating success rate, solution quality, and runtime trade-offs.

Proposed method

• The method begins with individually optimal trajectories for each robot, ignoring inter-robot collisions.
• It introduces a k-step penalty mechanism that increases the cost of trajectory segments that come close to other robots’ paths.
• The penalty is incrementally increased over iterations, and each robot’s trajectory is replanned after each penalty update to avoid conflict regions.
• The process continues until a collision-free solution is found, with the penalty tending toward infinity in the limit.
• The algorithm uses a dynamic environment model where higher-priority robots are treated as moving obstacles during replanning.
• The k parameter controls the number of iterations and penalty escalation steps, influencing solution quality and runtime.

Experimental results

Research questions

• RQ1 Can a penalty-based iterative method achieve near-optimal solution quality in multi-robot path planning while maintaining scalability?
• RQ2 How does the kPM method compare in solution cost and success rate to prioritized planning and ORCA on benchmark instances?
• RQ3 To what extent does increasing the number of penalty iterations (k) improve solution quality and convergence toward optimality?
• RQ4 Does the method scale effectively to larger robot counts compared to optimal or prioritized approaches?

Key findings

• On instances where the optimal solution is known, kPM with k=100 converges to solutions within 4–10% of the optimal cost.
• For instances without known optima, kPM produces trajectories that are 4–10% cheaper than those from prioritized planning.
• kPM reduces trajectory cost by up to 40% compared to ORCA, especially in high-density scenarios.
• kPM achieves a success rate of 88% on 20-robot instances in empty environments, compared to only 28% for prioritized planning.
• The method scales better than optimal algorithms like OD, which fail beyond three robots, and outperforms prioritized planning in both solution quality and success rate.
• In real-world environments—such as an office corridor and logistic center—kPM successfully coordinated 16 and 35 robots in 19 and 55 seconds, respectively, producing feasible, low-cost trajectories.