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 Frechet 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 Frechet 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.