完整与非完整约束下动力学方程的统一构建及求解OA

Holonomic and nonholonomic constraints often coexist in robot systems,especially in wheeled robot systems.A dynamic modeling method is proposed based on the Lagrange equations of the first kind with multipliers,which can simultaneously incorporate both holonomic and nonholonomic constraints and solve the generalized constraint forces between spatial rigid bodies.The forms of holonomic and nonholonomic constraints in the dynamics equations are distinguished,and the definitions of the constraint Jacobian matrix and the right-hand side matrix of acceleration constraints are given for these two types of constraints.Both constraint types are embedded into a unified dynamic framework,and a solution algorithm is proposed to obtain the generalized constraint forces of each rigid body.A simulation experiment is conducted with a thick wheel performing pure rolling on the ground.The proposed method is used for dynamic modeling and solving,and the generalized constraint forces exerted by the ground on the wheel are obtained,including the friction force,support force,and torque about the wheel′s center of mass.Simulation results show that the proposed method can handle both holonomic and nonholonomic constraints simultaneously,and the solved generalized constraint forces between spatial rigid bodies are consistent with mechanical principles,verifying the effectiveness of the method.This method is applicable to all multi-rigid-body systems and exhibits high generality.