As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and actuation errors compound to the errors introduced while estimating features of the environment. We present a novel approach (1) to incorporate these uncertainties for robot state estimation and (2) to compute the probability of collision pertaining to the estimated robot configurations. The expression for collision probability is obtained as an infinite series and we prove its convergence. An upper bound for the truncation error is also derived and the number of terms required is demonstrated by analyzing the convergence for different robot and obstacle configurations. We evaluate our approach using two simulation domains which use a roadmap-based strategy to synthesize trajectories that satisfy collision probability bounds.

翻译：由于机器人越来越多地在接近人类和物体的地方使用,因此机器人必须在现实世界条件下安全有效地运作,然而,环境却鲜为人知。在估计环境特征时,噪音传感器和动因错误会增加在估计环境特征时引入的错误。我们提出了一个新颖的方法:(1) 将这些不确定性纳入机器人状态估计,(2) 计算与估计机器人配置有关的碰撞概率。碰撞概率的表达方式是无限的系列,我们证明它已经趋同。还得出了截断错误的上限,分析不同机器人和障碍配置的趋同,从而显示所需条件的数量。我们用两个模拟领域来评估我们的方法,这两个领域使用基于路线图的战略来合成满足碰撞概率界限的轨迹。