  This paper presents a motion planning algorithm for quadruped locomotion
based on density functions. We decompose the locomotion problem into a
high-level density planner and a model predictive controller (MPC). Due to
density functions having a physical interpretation through the notion of
occupancy, it is intuitive to represent the environment with safety
constraints. Hence, there is an ease of use to constructing the planning
problem with density. The proposed method uses a simplified model of the robot
into an integrator system, where the high-level plan is in a feedback form
formulated through an analytically constructed density function. We then use
the MPC to optimize the reference trajectory, in which a low-level PID
controller is used to obtain the torque level control. The overall framework is
implemented in simulation, demonstrating our feedback density planner for
legged locomotion. The implementation of work is available at
\url{https://github.com/AndrewZheng-1011/legged_planner}
