Risk-Aware Non-Myopic Motion Planner for Large-Scale Robotic Swarm Using CVaR Constraints

TL;DR

The paper addresses safe, scalable motion planning for large-scale robotic swarms in cluttered environments. It introduces ROVER, a risk-aware, non-myopic planner that represents the swarm as a Gaussian Mixture Model and enforces collision avoidance through CVaR constraints within a finite-time MPC framework. A key contribution is the analytical GMM-CVaR formulation, enabling online optimization via Sequential Linear Programming by linearizing the CVaR constraint around feasible points. Simulations demonstrate that ROVER achieves robust safety with improved flexibility (splitting/merging) and scalability, maintaining online performance (≈1 Hz) while handling thousands of robots. This approach advances large-scale swarm planning by integrating probabilistic swarm representations, risk-aware constraints, and efficient online solution techniques.

Abstract

Swarm robotics has garnered significant attention due to its ability to accomplish elaborate and synchronized tasks. Existing methodologies for motion planning of swarm robotic systems mainly encounter difficulties in scalability and safety guarantee. To address these limitations, we propose a Risk-aware swarm mOtion planner using conditional ValuE at Risk (ROVER) that systematically navigates large-scale swarms through cluttered environments while ensuring safety. ROVER formulates a finite-time model predictive control (FTMPC) problem predicated upon the macroscopic state of the robot swarm represented by a Gaussian Mixture Model (GMM) and integrates conditional value-at-risk (CVaR) to ensure collision avoidance. The key component of ROVER is imposing a CVaR constraint on the distribution of the Signed Distance Function between the swarm GMM and obstacles in the FTMPC to enforce collision avoidance. Utilizing the analytical expression of CVaR of a GMM derived in this work, we develop a computationally efficient solution to solve the non-linear constrained FTMPC through sequential linear programming. Simulations and comparisons with representative benchmark approaches demonstrate the effectiveness of ROVER in flexibility, scalability, and risk mitigation.

Figures (4)

• Figure 1: Figure (a) illustrates the task of large-scale robotic swarm motion planning through a cluttered environment, with dashed lines indicating swarm transport trajectories and white dots denoting individual robots. Obstacles are represented as grey polygons. Figure (b) illustrates the first-person view in the red circular sector in Figure (a).
• Figure 2: Illustration of ROVER transporting the robot swarm from an initial area in the left column to the target area in the right column in a cluttered workspace $\mathcal{W}\subset\mathbb{R}^2$. Static obstacles are denoted by pale yellow polygons. Columns separated by verticle black lines correspond to different time steps. (a) Macroscopic planning in ROVER. Blue clouds represent the GMM distributions $\wp$ of the swarm state. Blue dashed lines illustrate the GMM transformation from $\wp_k$ to $\wp_{k+1}$, while the dash-dotted lines represent $(h-1)$ subsequent transformations from $\wp_{k+1}$ to $\wp_{k+h}$. The dotted lines represent the transformation from $\wp_{k+h}$ to $\wp_{targ}$. (b) Collision avoidance between GMM and obstacles using CVaR. The random variable $\zeta$ represents the distribution of distance between a GMM and obstacles. The shaded area denotes the $\alpha \%$ of the area under $p(\zeta)$. The collision avoidance under a risk acceptance level $\alpha\in(0,1]$ is to constrain the $CVaR_\alpha(\zeta)$, the expected value of $\zeta$ under the shaded area, below a user-defined threshold $\epsilon$. (c) Microscopic control in ROVER. Robots track the GMM trajectories given from the macroscopic level while avoiding collision.
• Figure 3: An example of determining $\mathcal{GC}_k$ and $N_k$, $\forall k\in \underline{T_f}$, based on \ref{['ass:GC-set']} and \ref{['ass:N_GC']}. Figures (a), (b), and (c) represent GMMs at time steps $k$, $k+1$, and $k+2$, respectively. Light blue circles depict GCs in $\mathcal{C}$ and pentagrams with numbers represent the GCs at specific time step and their corresponding indices. The dotted lines give an example of weight transported between consecutive time steps within a transport range denoted by light orange circles.
• Figure 4: Figure (a)-(c) shows the trajectories of 500 robots generated by ROVER, FC, and PC, respectively. The initial positions of robots are demonstrated by circles, while their corresponding final positions are highlighted by diamonds. The grey polygons denote static obstacles.

Theorems & Definitions (4)

• Proposition 1
• Proposition 2
• proof
• proof