Following Paths in Task Space: Distance Metrics and Planning Algorithms

Many of our everyday jobs we imagine robots accomplishing are defined via a variety of task-specific constraints. In order for robots to perform these tasks, the robot’s motion planners must respect these constraints. While a robotic manipulator moves and plans in its joint or configuration space, many constraints are naturally defined in task space. We focus on the specific constraint asking the robot’s end effector (hand) to trace out a shape. Formally, our goal is to produce a configuration space path that closely follows a desired task space path despite the presence of obstacles. This thesis proposes distance metrics for formally defining closeness and planning algorithms that efficiency leverage these definitions. Adapting metrics from computational geometry, we show that the discrete Fréchet distance metric is an effective and natural tool for capturing the notion of closeness between two paths in task space. We then introduce two algorithmic approaches for efficiently planning with this metric. The first is a trajectory optimization approach that directly optimizes to minimize the Fréchet distance between the produced path and the desired task space path. The second approach searches along a configuration space embedding graph of the task space path. Finally, we evaluate these approaches through real robot and simulation experiments.