Deterministic methods for motion planning guarantee safety amidst uncertainty in obstacle locations by trying to restrict the robot from operating in any possible location that an obstacle could be in. Unfortunately, this can result in overly conservative behavior. Chance-constrained optimization can be applied to improve the performance of motion planning algorithms by allowing for a user-specified amount of bounded constraint violation. However, state-of-the-art methods rely either on moment-based inequalities, which can be overly conservative, or make it difficult to satisfy assumptions about the class of probability distributions used to model uncertainty. To address these challenges, this work proposes a real-time, risk-aware reachability-based motion planning framework called RADIUS. The method first generates a reachable set of parameterized trajectories for the robot offline. At run time, RADIUS computes a closed-form over-approximation of the risk of a collision with an obstacle. This is done without restricting the probability distribution used to model uncertainty to a simple class (e.g., Gaussian). Then, RADIUS performs real-time optimization to construct a trajectory that can be followed by the robot in a manner that is certified to have a risk of collision that is less than or equal to a user-specified threshold. The proposed algorithm is compared to several state-of-the-art chance-constrained and deterministic methods in simulation, and is shown to consistently outperform them in a variety of driving scenarios. A demonstration of the proposed framework on hardware is also provided.

翻译：确定性方法通过限制机器人避开障碍物可能占据的任何位置来保证不确定性环境下避障的安全性，但这可能导致过于保守的行为。机会约束优化允许用户指定有界约束违反量以提升运动规划算法性能，然而当前最先进的方法要么依赖基于矩的不等式（可能过于保守），要么难以满足不确定性建模中概率分布类别的假设。为应对这些挑战，本文提出一种名为RADIUS的实时风险感知可达性运动规划框架。该方法首先离线生成机器人参数化轨迹的可达集，运行时通过闭式超近似计算与障碍物碰撞风险，且不要求不确定性建模的概率分布限制于简单类型（如高斯分布）。随后，RADIUS执行实时优化以构建机器人可执行的轨迹，并保证其碰撞风险不超过用户指定的阈值。仿真实验将所提算法与多种先进的机会约束方法和确定性方法进行对比，结果表明其在多种驾驶场景中均具有更优表现。本文还提供了该框架的硬件实物验证。