The problem of planning sensing trajectories for a mobile robot to collect observations of a target and predict its future trajectory is known as active target tracking. Enabled by probabilistic motion models, one may solve this problem by exploring the belief space of all trajectory predictions given future sensing actions to maximise information gain. However, for multi-modal motion models the notion of information gain is often ill-defined. This paper proposes a planning approach designed around maximising information regarding the target's homotopy class, or high-level motion. We introduce homotopic information gain, a measure of the expected high-level trajectory information given by a measurement. We show that homotopic information gain is a lower bound for metric or low-level information gain, and is as sparsely distributed in the environment as obstacles are. Planning sensing trajectories to maximise homotopic information results in highly accurate trajectory estimates with fewer measurements than a metric information approach, as supported by our empirical evaluation on real and simulated pedestrian data.

翻译：移动机器人规划感知轨迹以收集目标观测并预测其未来轨迹的问题被称为主动目标跟踪。借助概率运动模型，可通过探索给定未来感知动作下所有轨迹预测的置信空间来最大化信息增益，从而解决该问题。然而，对于多模态运动模型，信息增益的概念往往定义不清。本文提出一种围绕最大化目标同伦类（即高层运动）信息进行规划的方案。我们引入了同伦信息增益，该指标衡量给定测量条件下预期的高层轨迹信息量。我们证明同伦信息增益是度量层面（即低层）信息增益的下界，且其在环境中的分布稀疏性与障碍物分布特性相似。通过在实际与模拟行人数据上的实证评估表明，规划感知轨迹以最大化同伦信息增益，相比基于度量信息的方案能以更少的测量次数获得更高精度的轨迹估计。