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：摘要：确定性运动规划方法通过限制机器人不在障碍物可能占据的任何位置运行，来保证障碍物位置不确定性下的安全性。然而，这可能导致过于保守的行为。机会约束优化可通过允许用户指定有限程度的约束违反，从而提升运动规划算法的性能。然而，现有方法要么依赖基于矩的不等式（可能过于保守），要么难以满足用于建模不确定性的概率分布类别的假设。为解决这些挑战，本文提出一种名为RADIUS的实时、风险感知的基于可达性的运动规划框架。该方法首先离线生成机器人的参数化轨迹可达集。在运行时，RADIUS计算与障碍物碰撞风险的闭式上近似，且不限制用于建模不确定性的概率分布为简单类别（如高斯分布）。随后，RADIUS执行实时优化以构建机器人可遵循的轨迹，该轨迹被认证其碰撞风险小于等于用户指定的阈值。所提算法在仿真中与多种先进的机会约束和确定性方法进行比较，并在多种驾驶场景中持续优于这些方法。此外，还提供了所提框架的硬件演示实验。