Safety in the face of uncertainty is a key challenge in robotics. In this work, we propose a real-time capable framework to generate safe and task-efficient robot trajectories for stochastic control problems. For that, we first formulate the problem as a chance-constrained optimisation problem, in which the probability of the controlled system to violate a safety constraint is constrained to be below a user-defined threshold. To solve the chance-constrained optimisation problem, we propose a Monte--Carlo approximation relying on samples of the uncertainty to estimate the probability of violating a safety constraint given a controller. We use this approximation in the motion planner VP-STO to solve the sampled-based problem. Consequently, we refer to our adapted approach as CC-VPSTO, which stands for Chance-Constrained VP-STO. We address the crucial issue concerning the Monte--Carlo approximation: given a predetermined number of uncertainty samples, we propose several ways to define the sample-based problem such that it is a reliable over-approximation of the original problem, i.e. any solution to the sample-based problem adheres to the original chance-constrained problem with high confidence. The strengths of our approach lie in i) its generality, as it does not require any specific assumptions on the underlying uncertainty distribution, the dynamics of the system, the cost function, and for some of the proposed sample-based approximations, on the form of inequality constraints; and ii) its applicability to MPC-settings. We demonstrate the validity and efficiency of our approach on both simulation and real-world robot experiments. For additional material, please visit https://sites.google.com/oxfordrobotics.institute/cc-vpsto.

翻译：面对不确定性时的安全性是机器人领域的关键挑战。本文提出了一种实时框架，用于在随机控制问题中生成安全高效的任务导向机器人轨迹。首先将问题建模为机会约束优化问题，其中受控系统违反安全约束的概率被限制在用户定义的阈值以下。为求解该问题，我们提出了一种基于不确定性样本的蒙特卡洛近似方法，用于估计给定控制器下违反安全约束的概率。我们将该近似方法集成到运动规划器VP-STO中求解基于样本的优化问题，由此提出的改进方法称为CC-VPSTO（Chance-Constrained VP-STO）。针对蒙特卡洛近似的关键问题——给定预设数量的不确定性样本，我们提出了多种定义样本问题的方法，使其能够可靠地过近似原始问题：即样本问题的任意解均能以高置信度满足原始机会约束问题。本方法的优势在于：i）通用性，无需对不确定性分布、系统动力学、代价函数以及部分提出的样本近似方法中的不等式约束形式作出特定假设；ii）适用于模型预测控制（MPC）场景。我们通过仿真实验和真实机器人实验验证了该方法的有效性和高效性。补充资料请访问https://sites.google.com/oxfordrobotics.institute/cc-vpsto。