摘要
冗余机械臂逆运动学求解需要规避关节极限,以确保解符合机械臂的实际物理限制.当前基于微分运动学的求解方法通常仅考虑局部瞬时状态,无法保证关节在连续运动过程中始终远离物理极限.为解决此问题,本文提出了一种基于模型预测的冗余机械臂逆运动学求解方法.通过结合雅可比矩阵零空间的参数化形式,有效地考虑了系统运动状态及约束的未来演变.针对关节物理限制,设计了约束条件与优化目标,进而将逆运动学求解转化为约束优化问题,充分利用冗余自由度实现关节极限规避.此外,为确保优化问题的可行性,采用任务缩放方法对末端速度违反约束的情况进行处理.基于七自由度冗余机械臂的仿真实验结果表明,相较于基准方法,所提方法能够预测并规避潜在的关节极限违反,同时准确跟踪末端目标轨迹.
The inverse kinematics of redundant manipulators must avoid joint limits to ensure solutions comply with the actual physical constraints.Conventional based on differential kinematicsbased methods typically consider only local instantaneous states and cannot guarantee that the joints remain within the physical limits throughout continuous motion.To address this issue,this paper proposes an inverse kinematics method for redundant manipulators based on model predictive control.By combining the null space parameterization of the Jacobian matrix,the proposed method effectively accounts for the future evolution of the system’s kinematic states and constraints.The constraints and optimization objective functions are designed to handle joint limits.The inverse kinematics problem is transformed into a constrained optimization problem,where redundancy is fully exploited to avoid joint limits.Furthermore,to ensure the feasibility of the optimization problem,a task scaling method is introduced to handle violations of constraints by the end-effector velocity.Simulation results on a 7-DOF redundant manipulator demonstrate that,compared with benchmark methods,the proposed method can predict and avoid potential joint limit violations while accurately tracking the target trajectory of the end-effector.
作者
孙浩翔
王笑
宋汉文
Sun Haoxiang;Wang Xiao;Song Hanwen(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)
出处
《动力学与控制学报》
2025年第10期45-52,共8页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(12272266,U2441202,12402003)。
关键词
冗余机械臂
逆运动学
模型预测控制
关节极限
redundant manipulator
inverse kinematics
model predictive control
joint limits
