移动机械臂运动学建模与控制

Kinematic molding and control for mobile manipulator

针对冗余移动机械臂的轨迹跟踪问题,通过闭环算法对移动机械臂沿给定末端执行器轨迹与始末姿态的运动进行了研究。将移动底座与机械臂视为一个系统建立运动学模型,由于任务空间速度与关节空间速度没有直接的运动学映射,推导了通用形式的几何雅可比矩阵。给定单位四元数形式的始末姿态,并定义四元数下的姿态误差,通过四元数插值得到离散形式的姿态,并由四元数微分求得角速度。利用关节极限约束对零空间进行修正,使关节变量尽可能接近其范围中点。针对末端轨迹为直线与曲线两种情况,利用伪逆方法的闭环逆运动学算法求解相应的移动底座轨迹与关节轨迹。研究结果表明,该算法具有可行性与有效性。

Aiming at the trajectory tracking problem of redundant mobile manipulator,the motion of redundant mobile manipulator along given end-effector path and its initial and final orientation is investigated by the means of a closed-loop algorithm.We consider the mobile manipulator as one system to build the kinematic molding.Since there is no direct kinematic mapping between task-space velocity and joint-space velocity,a general Jacobian matrix is derived.Given the initial and final orientation in the quaternion form,and then we define the orientation error.We can obtain the discrete orientation through quaternion interpolation and the angular velocity through quaternion differentiation.The constraints of joint limts are applied to modify the null space,which can keep the joint variables as close as possible to the centre of their ranges.Aiming as the two cases where the end-effector paths is straight line and a curve,the closed-loop inverse kinematics algorithm(CLIK)via pseudoinverse method is used to solve the mobile base trajectories and joint trajectories.The simulation results demonstrate the feasibility and effectiveness of the proposed algorithm.