Control Barrier Functions (CBF) are a powerful tool for designing safety-critical controllers and motion planners. The safety requirements are encoded as a continuously differentiable function that maps from state variables to a real value, in which the sign of its output determines whether safety is violated. In practice, the CBFs can be used to enforce safety by imposing itself as a constraint in a Quadratic Program (QP) solved point-wise in time. However, this approach costs computational resources and could lead to infeasibility in solving the QP. In this paper, we propose a novel motion planning framework that combines sampling-based methods with Linear Quadratic Regulator (LQR) and CBFs. Our approach does not require solving the QPs for control synthesis and avoids explicit collision checking during samplings. Instead, it uses LQR to generate optimal controls and CBF to reject unsafe trajectories. To improve sampling efficiency, we employ the Cross-Entropy Method (CEM) for importance sampling (IS) to sample configurations that will enhance the path with higher probability and store computed optimal gain matrices in a hash table to avoid re-computation during rewiring procedure. We demonstrate the effectiveness of our method on nonlinear control affine systems in simulation.
翻译:控制区域函数 (CBF) 是设计安全关键控制器和运动规划的强大工具。安全要求被编码为从状态变量到实数值的连续可微函数,其中其输出的符号确定是否违反了安全性。实际上,CBF 可用于通过将其作为在时间点上求解的二次规划 (QP) 中的约束来强制执行安全性。然而,这种方法的计算成本很高,并且在求解 QP 时可能会导致不可行性。在本文中,我们提出了一种新颖的运动规划框架,将采样法方法与线性二次调节器 (LQR) 和 CBF 结合起来。我们的方法不需要解决用于控制合成的 QP 并避免在采样过程中进行显式的碰撞检测。相反,它使用 LQR 生成最优控制和 CBF 拒绝不安全的轨迹。为了提高采样效率,我们采用交叉熵 (CEM) 用于重要性采样 (IS),以采样将提高路径概率的配置,并在哈希表中存储计算的最优增益矩阵,以避免在重连过程中重新计算。我们在仿真中展示了我们方法在非线性控制仿射系统上的有效性。