We consider the problem of safely coordinating ensembles of identical autonomous agents to conduct complex missions with conflicting safety requirements and under noisy control inputs. Using non-smooth control barrier functions (CBFs) and stochastic model-predictive control as springboards and by adopting an extrinsic approach where the ensemble is treated as a unified dynamic entity, we devise a method to synthesize safety-aware control inputs for uncertain collectives, drawing upon recent developments in Boolean CBF composition and extensions of CBFs to stochastic systems. Specifically, we approximate the combined CBF by a smooth function and solve a stochastic optimization problem, with agent-level forcing terms restricted to the resulting affine subspace of safe control inputs. For the smoothing step, we employ a polynomial approximation scheme, providing evidence for its advantage in generating more conservative yet sufficiently-filtered control signals than the smoother but more aggressive equivalents realized via an approximation technique based on the log-sum-exp function. To further demonstrate the utility of the proposed method, we present bounds for the expected value of the CBF approximation error, along with results from simulations of a single-integrator collective under velocity perturbations, comparing these results with those obtained using a naive state-feedback controller lacking safety filters.

翻译：本文研究在存在冲突安全约束和噪声控制输入的情况下，安全协调同构自主智能体集群执行复杂任务的问题。以非光滑控制势垒函数（CBF）和随机模型预测控制为基础，通过采用将集群视为统一动态实体的外源性方法，结合布尔CBF组合的最新进展及CBF向随机系统的扩展，提出一种为不确定性集群合成安全感知控制输入的方法。具体而言，我们将组合CBF通过光滑函数逼近，并求解随机优化问题，其中智能体级别的强迫项被限制在由此生成的安全控制输入仿射子空间中。在光滑化步骤中，我们采用多项式逼近方案，论证其在生成更保守但充分滤噪的控制信号方面，优于基于对数-求和-指数函数的逼近技术所实现的更平滑但更具侵略性的等效方案。为进一步展示所提方法的实用性，我们给出了CBF逼近误差期望值的界，以及速度扰动下单积分器集群的仿真结果，并与采用缺乏安全滤波器的朴素状态反馈控制器所得结果进行比较。