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}

翻译：本文提出了一种基于密度函数的四足运动规划算法。我们将运动问题分解为高层密度规划器与模型预测控制器（MPC）。由于密度函数通过占用概念具有直观的物理解释，因此能够自然地通过安全约束描述环境，从而便于利用密度构建规划问题。所提方法将机器人简化为积分器系统，其中高层规划采用通过解析构造的密度函数形成的反馈形式。随后我们使用MPC对参考轨迹进行优化，并通过底层PID控制器实现力矩级控制。整体框架在仿真中实现，验证了所提出的用于足式运动的反馈密度规划器。本工作实现代码见：\url{https://github.com/AndrewZheng-1011/legged_planner}