Safe Interval RRT* for Scalable Multi-Robot Path Planning in Continuous Space

TL;DR

The paper tackles scalable MRPP in continuous spaces by introducing a two-level framework: a low-level SI-RRT^* planner for individual robots and high-level conflict-resolution methods SI-CPP and SI-CCBS to coordinate multiple robots. SI-RRT^* achieves probabilistic completeness and asymptotic optimality by leveraging safe intervals to avoid discretizing time, enabling efficient planning in 2D/3D spaces and accommodating kinodynamic extensions via a local planner. SI-CPP emphasizes scalability, handling large robot teams (up to ~160) with fast success rates, while SI-CCBS focuses on solution quality through a CBS-style search that re-plans to reduce conflicts. Experimental results across four environments show SI-CPP and SI-CCBS significantly outperform state-of-the-art baselines in success rate, flowtime, and makespan, highlighting the framework’s practical impact for dense, real-world MRPP scenarios and paving the way for physical-robot validation.

Abstract

In this paper, we consider the problem of Multi-Robot Path Planning (MRPP) in continuous space. The difficulty of the problem arises from the extremely large search space caused by the combinatorial nature of the problem and the continuous state space. We propose a two-level approach where the low level is a sampling-based planner Safe Interval RRT* (SI-RRT*) that finds a collision-free trajectory for individual robots. The high level can use any method that can resolve inter-robot conflicts where we employ two representative methods that are Prioritized Planning (SI-CPP) and Conflict Based Search (SI-CCBS). Experimental results show that SI-RRT* can quickly find a high-quality solution with a few samples. SI-CPP exhibits improved scalability while SI-CCBS produces higher-quality solutions compared to the state-of-the-art planners for continuous space.

Figures (7)

• Figure 1: Challenging instances with 160 robots where robots often experience conflicts. These are also test environments Circ10, Circ20, Rect10, and Rect20 used in our experiments.
• Figure 2: An illustration of the safe interval at $\boldsymbol q$. The interval is defined for $h^i(\boldsymbol q)$ to consider the size of robot $i$ at $\boldsymbol q$. The robot can stay at $\boldsymbol q$ without a collision during the safe interval (green). The shapes of the robot and dynamic obstacles, as well as the trajectory of the obstacle, can be arbitrary.
• Figure 3: An illustration showing how $low$ is determined in ChooseParent. (Left) The robot can stay $v$ from $v.t_{\text{low}}$ until $\iota.high$ without collisions. The SI of $v_\text{new}.\boldsymbol q$ is $[\iota_\text{new}.low, \iota_\text{new}.high)$. (Right) The bold arrow represents a trajectory to move from $v.\boldsymbol q$ to $v_\text{new}.\boldsymbol q$ as early as possible without colliding with the blue dynamic obstacle. Thus, $low$ is the earliest arrival time at $v_\text{new}.\boldsymbol q$ along the trajectory.
• Figure 4: A comparison between SI-RRT$^*$ (yellow) and ST-RRT$^*$ (green) for single-robot path planning in the four test environments. The earliest arrival time at the goal of SI-RRT$^*$ decreases faster than ST-RRT$^*$, indicating that SI-RRT$^*$ can find better trajectories faster.
• Figure 5: The success rates of compared methods under five minutes of the time limit. The proposed method SI-CPP succeeds in almost all instances, even in congested environments. As the advantage of SI-CCBS is in its solution quality, its success rates are lower than SI-CPP and ST-RRT$^*$ -PP but significantly higher than SSSP and GT.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof