Current motion planning approaches rely on binary collision checking to
evaluate the validity of a state and thereby dictate where the robot is allowed
to move. This approach leaves little room for robots to engage in contact with
an object, as is often necessary when operating in densely cluttered spaces. In
this work, we propose an alternative method that considers contact states as
high-cost states that the robot should avoid but can traverse if necessary to
complete a task. More specifically, we introduce Contact Admissible
Transition-based Rapidly exploring Random Trees (CAT-RRT), a planner that uses
a novel per-link cost heuristic to find a path by traversing high-cost obstacle
regions. Through extensive testing, we find that state-of-the-art optimization
planners tend to over-explore low-cost states, which leads to slow and
inefficient convergence to contact regions. Conversely, CAT-RRT searches both
low and high-cost regions simultaneously with an adaptive thresholding
mechanism carried out at each robot link. This leads to paths with a balance
between efficiency, path length, and contact cost