The field of swarm robotics has attracted considerable interest for its capacity to complete intricate and synchronized tasks. Existing methodologies for motion planning within swarm robotic systems mainly encounter difficulties in scalability and safety guarantee. To address these two limitations, we propose a Risk-aware swarm mOtion planner using conditional ValuE at Risk (ROVER) that systematically modulates the safety and conservativeness and navigates the swarm to the target area through cluttered environments. Our approach formulates a finite-time model predictive control (FTMPC) problem predicated upon the macroscopic state of the robot swarm represented by Gaussian Mixture Model (GMM) and integrates conditional value-at-risk (CVaR) to avoid collision. We leverage the linearized Signed Distance Function for the efficient computation of CVaR concerning the proximity between the robot swarm to obstacles. The key component of this method is implementing CVaR constraint under GMM uncertainty in the FTMPC to measure the collision risk that a robot swarm faces. However, the non-convex constrained FTMPC is nontrival to solve. To navigate this complexity, we develop a computationally tractable strategy through 1) an explicit linear approximation of the CVaR constraint; and 2) a sequential quadratic programming formulation. Simulations and comparisons with other approaches demonstrate the effectiveness of the proposed method in flexibility, scalability, and risk mitigation.

翻译：群体机器人技术因能够完成复杂且协调的任务而受到广泛关注。现有群体机器人系统的运动规划方法主要面临可扩展性和安全保障两方面的挑战。为解决这两大局限性，我们提出了一种基于条件风险值的风险感知群体运动规划器（ROVER），该规划器能够系统性地调节安全性与保守性，并引导群体通过杂乱环境向目标区域移动。我们的方法基于高斯混合模型（GMM）表征的机器人群体宏观状态，构建了有限时间模型预测控制（FTMPC）问题，并集成条件风险值（CVaR）以避免碰撞。我们利用线性化符号距离函数高效计算机器人群体与障碍物接近度相关的CVaR。该方法的核心在于：在FTMPC框架中，将基于GMM不确定性的CVaR约束作为风险度量指标，评估机器人群体面临的碰撞风险。然而，非凸约束的FTMPC求解具有较大挑战。为应对这一复杂性，我们开发了一种可计算的高效策略，包括：1）CVaR约束的显式线性近似；2）序列二次规划求解方案。仿真实验及与其他方法的对比结果表明，该方法在灵活性、可扩展性和风险缓解方面具有显著有效性。