  Inspired by the utilization of dogs in sled-pulling for transportation, we
introduce a cable-trailer system with a quadruped robot. The motion planning of
the proposed robot system presents challenges arising from the nonholonomic
constraints of the trailer, system underactuation, and hybrid interaction
through the cable. To tackle these challenges, we develop a hybrid dynamics
model that accounts for the cable's taut/slack status. Since it is
computationally intense to directly optimize the trajectory, we first propose a
search algorithm to compute a sub-optimal trajectory as the initial solution.
Then, a novel collision avoidance constraint based on the geometric shapes of
objects is proposed to formulate the trajectory optimization problem for the
hybrid system. The proposed trajectory planning method is implemented on a
Unitree A1 quadruped robot with a customized cable-trailer and validated
through experiments.
