An optimized inverse kinematic algorithm was developed for 7 degrees of freedom (7-DoF) manipulators with an S-R-S kinematic structure that avoids joint limits. The first step determines the closed-form solution of the inverse kinematics model based on the arm angle parameter. The result is then used to determine feasible arm angle intervals for the given joint limits. Then, an optimal weighted target function is defined to avoid the joint limits with the weights determined according to the joint positions. The relations between the joint angles and the arm angles are then linearized to simplify the complex optimal target function to a quadratic function. The optimization problem that includes the feasible arm angle intervals then avoids the joint limit. This intuitive, efficient algorithm is effective, avoids the joint limits and can be computed online.
胡奎,张继文,董云飞,吴丹. 针对关节限位优化的7自由度机械臂逆运动学解法[J]. 清华大学学报（自然科学版）, 2020, 60(12): 1007-1015.
Kui HU,Jiwen ZHANG,Yunfei DONG,Dan WU. Inverse kinematic optimization for 7-DoF serial manipulators with joint limits. Journal of Tsinghua University(Science and Technology), 2020, 60(12): 1007-1015.
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