基于对偶二次规划的六足并联机器人驱动力分配

Optimal Driving Forces Distribution for a Six-parallel-legged Robot Based on Dual Quadratic Programming Method

针对六足并联机器人冗余驱动问题,提出以降低能耗,提高承载能力为目标的驱动力优化分配方法。通过建立六足并联机器人运动学与动力学模型,得到机器人关节驱动力与脚力间转换关系。在分析机器人动态平衡条件并考虑摩擦约束、最大驱动力约束及触地约束的基础上,建立以驱动力平方和最小为目标函数的二次规划问题。基于QR分解的广义消去法消去等式约束减少约束方程的数量以提高优化问题的求解速度,采用对偶理论将问题转化为对偶二次规划问题可以进一步提高求解速度。分析了多足机器人与多指灵巧手动力学模型的不同,因此两者的二次规划目标函数也存在不同。同时与传统的以内力最小为目标函数的方法比较,表明该方法能够充分利用地面摩擦力以减小驱动力,从而提高承载能力,降低能量消耗。

The active forces distribution algorithm for improving bearing capability and minimizing energy consumption is proposed to solve the redundant actuation problem of a six-parallel-legged robot. The transformation between active joint forces and foot contact forces is established based on the kinematic model and dynamic model. After analyzing the force/moment equilibrium equations of the robot, the quadratic programming optimization model is obtained considering the constraints of friction cone, unilateral constraint and the limits of motors’ torques. The solving time of the quadratic programming is reduced by eliminating and simplifying equality and inequality constraints using elimination method based on QR decomposition and dual method. The difference between the objective function of multi-legged robots and multi-finger hands is pointed out because of the difference of their dynamic models. Compared with the traditional method, the proposed algorithm has great advantages in improving bearing capability and minimizing energy consumption due to the efficient utilizing of the contact friction forces.