基于QP优化的双轮腿–单臂机器人全身运动规划

Whole-Body Motion Planning for a Two-Wheeled-Legged Single-Arm Robot: A QP-Based Approach

摘要: 针对双轮腿–单臂机器人在全身运动规划中的自由度冗余问题，本文提出了一种基于二次规划(QP)优化的运动规划方法。该方法将躯干运动视为机械臂运动链的延伸，将手臂与躯干作为一个整体运动系统进行建模与控制。以TITA-PiPER机器人为研究对象，首先，通过建立机械臂末端位姿与七维广义关节速度之间的雅可比矩阵映射，并将该映射关系作为硬约束，以确保手臂末端任务具有最高优先级。然后，构造以关节运动平滑性为优化目标，同时融合关节限位、非完整约束及动态平衡稳定性的二次规划问题，从而统一求解出满足整体运动要求的七维广义关节加速度。仿真结果表明，该方法能够在保证手臂末端任务精确执行的同时，充分利用躯干的运动能力实现全身协调，为轮腿臂机器人的实时运动控制提供了有效的解决方案。

Abstract: In addressing the redundancy of degrees of freedom in whole-body motion planning for a two-wheeled-legged single-arm robot, this paper proposes a motion planning method based on Quadratic Programming (QP) optimization. This approach treats the torso motion as an extension of the robotic arm’s kinematic chain, modeling and controlling the arm and torso as an integrated motion system. Taking the TITA-PiPER robot as the subject of study, a Jacobian matrix mapping between the end-effector pose of the arm and the velocities of the seven-dimensional generalized joints is first established. This mapping is enforced as a hard constraint to guarantee the highest priority for the end-effector task. Subsequently, a QP problem is formulated. It minimizes joint motion jerk (or another smoothness metric) as the optimization objective while incorporating constraints such as joint limits, nonholonomic constraints, and dynamic balance stability. This framework allows for the unified solving of the seven-dimensional generalized joint accelerations that satisfy the overall motion requirements. Simulation results demonstrate that the proposed method ensures precise execution of the end-effector task while fully utilizing the torso’s mobility to achieve whole-body coordination. It provides an effective solution for the real-time motion control of wheeled-legged robots with an arm.