We present an approach for safe motion planning under robot state and environment (obstacle and landmark location) uncertainties. To this end, we first develop an approach that accounts for the landmark uncertainties during robot localization. Existing planning approaches assume that the landmark locations are well known or are known with little uncertainty. However, this might not be true in practice. Noisy sensors and imperfect motions compound to the errors originating from the estimate of environment features. Moreover, possible occlusions and dynamic objects in the environment render imperfect landmark estimation. Consequently, not considering this uncertainty can wrongly localize the robot, leading to inefficient plans. Our approach thus incorporates the landmark uncertainty within the Bayes filter estimation framework. We also analyze the effect of considering this uncertainty and delineate the conditions under which it can be ignored. Second, we extend the state-of-the-art by computing an exact expression for the collision probability under Gaussian distributed robot motion, perception and obstacle location uncertainties. We formulate the collision probability process as a quadratic form in random variables. Under Gaussian distribution assumptions, an exact expression for collision probability is thus obtained which is computable in real-time. In contrast, existing approaches approximate the collision probability using upper-bounds that can lead to overly conservative estimate and thereby suboptimal plans. We demonstrate and evaluate our approach using a theoretical example and simulations. We also present a comparison of our approach to different state-of-the-art methods.

翻译：我们提出了一种在机器人状态与环境（障碍物和地标位置）不确定性条件下实现安全运动规划的方法。为此，我们首先发展了一种在机器人定位过程中考虑地标不确定性的方法。现有规划方法通常假设地标位置完全已知或仅存在微小不确定性，然而实际场景中这往往难以成立。噪声传感器和运动误差会加剧环境特征估计的误差累积，同时环境中的潜在遮挡和动态物体会导致地标估计不完善。若不考虑此类不确定性，机器人定位可能出现偏差，进而产生低效规划。因此，我们的方法将地标不确定性纳入贝叶斯滤波估计框架，并分析了考虑该不确定性的影响，界定了可忽略其影响的条件。其次，我们通过计算机器人运动、感知和障碍物位置均服从高斯分布时的碰撞概率精确表达式，拓展了现有技术水平。我们将碰撞概率过程构造成随机变量的二次型形式，在高斯分布假设下推导出可实时计算的碰撞概率精确表达式。相比之下，现有方法采用上界近似碰撞概率，可能导致过度保守估计和次优规划。我们通过理论示例与仿真验证了该方法，并将其与多种前沿方法进行了对比分析。