基于旋量理论和Paden-Kahan子问题的6自由度机器人逆解算法

Algorithm for the Inverse Kinematics Calculation of 6-DOF Robots Based on Screw Theory and Paden-Kahan Sub-problems

机器人逆解中运动学模型的建立主要采用Denavit-Hartenberg(D-H)参数法和旋量法。D-H参数法相对成熟,在机器人运动学分析中得到广泛应用。旋量法实际应用相对较少,但旋量法中机器人各连杆坐标系相对于底座建立,具有明确的几何意义。基于旋量法建立起的机器人运动学模型,其逆解常采用Paden-Kahan子问题方法加以求解,单纯的Paden-Kahan子问题法只能解决低自由度机器人的逆解。针对后三个关节相交于一点的6自由度关节机器人,基于旋量理论建立起机器人运动学模型,利用经典消元理论和Paden-Kahan子问题相结合的方法,提出一种机器人运动学逆解算法,并给出此类机器人运动学逆解的显式求解结果。以库卡KR-150机器人为例,利用该算法进行运动学逆解,验证了算法的正确性。

Denavit-Hartenberg（D-H） notation method and screw theory method are usually used to set up the kinematics model of a robot when its inverse kinematics calculation is to be carried out. D-H method is relatively mature and wildly used in kinematics analysis of robots. Screw method is relatively less in practical application, but with this method, the coordinate of each link of the robot is set up with reference to the base of the robot, so the coordinate has definite geometric meaning. For the kinematics model set up by screw method, the inverse kinematics calculation is usually realized by using Paden-Kahan sub-problem method. Pure Paden-Kahan sub-problems method can only be used for the inverse kinematics calculation of robot with low-DOE The kinematics model of the robot with 6-DOF and with the last three joint axes intersecting to one point is set up by using screw method, and a new algorithm is proposed for the inverse kinematics calculation of this kind of robot, by using the combined method of algebraic elimination method and Paden-Kahan sub-problem method, and the result of explicit solution is given. The correctness of the algorithm is verified by KUKA KR-150 robot, whose kinematics mode is set up by using the proposed algorithm.