有关节约束超冗余机械臂的增益优化轨迹规划
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摘要
为了实现超冗余机械臂的实时在线规划,本文提出一种基于雅克比转置矩阵的人工势场轨迹规划方法。轨迹规划不仅要满足末端跟踪精度要求,而且要满足关节速度和角度约束,关节速度主要由轨迹规划算法的增益决定,而增益的大小决定系统稳态性能的好坏,通过优化势场函数和使用加权关节速度,在避免关节限制的前提下减小关节速度范数,从而能选择更大的增益。使用蒙特卡洛法建立最大关节速度与增益的关系,从而确定增益范围。分别在点对点运动和轨迹跟踪运动中选取不同的增益证明算法的正确性和有效性,并在轨迹跟踪运动中引入速度前馈,通过李雅普诺夫稳定性定理证明算法稳定性。通过以超冗余机械臂为模型仿真验证,得出在点对点运动下末端位置偏差小于10~(-4)mm,姿态偏差小于1×10~(-5)rad;轨迹跟踪运动的位置偏差小于10~(-3)mm,姿态偏差小于1×10~(-4)rad。最后进行实验验证,虽然实验过程中轨迹偏差相比于仿真增加一个数量级,但仍符合实验任务需求。
Because their inverse kinematics do not have analytical solutions,hyper-redundant manipulators cannot be directly solved by the geometric method.To realize real-time planning,this study proposes an artificial potential field trajectory planning method based on the Jacobian transposition matrix.Trajectory planning must satisfy not only the requirements of end-tracking accuracy but also the joint velocity and angular constraints.The joint velocity is mainly determined by the gain of the trajectory planning algorithm.Through the optimization of the potential field function and use of weighted joint velocities,the joint speed norms can be reduced under the precondition of avoiding joint restriction.Thus,a larger gain can be selected to help the system achieve a better steady-state performance.The Monte Carlo method was used to establish the relationship between the maximum joint speed and gain,which is necessary to determine the gain range for selecting an appropriate gain.The correctness and effectiveness of the algorithm can be proved by selecting different gains in point-topoint and trajectory tracking motion.The study also introduces velocity feedforward in trajectory tracking motion and proves the stability of the two motion formal algorithms by the Lyapunov stability theorem.Results of a simulation verification of the hyper-redundant manipulator independently designed and manufactured by our laboratory revealed that the end position deviation and attitude deviation were less than 10~(-4)mm and 1×10~(-5)rad,respectively,based on the premise of ensuring rapid point-to-point movement.In addition,the trajectory tracking movement position deviation and altitude deviation were less than 10~(-3)mm and 1×10~(-4)rad,respectively.Finally,experimental verification revealed that although the trajectory deviation in the experimental process increased by an order of magnitude compared to the simulation,the requirements of the experimental task were still met.
Because their inverse kinematics do not have analytical solutions,hyper-redundant manipulators cannot be directly solved by the geometric method.To realize real-time planning,this study proposes an artificial potential field trajectory planning method based on the Jacobian transposition matrix.Trajectory planning must satisfy not only the requirements of end-tracking accuracy but also the joint velocity and angular constraints.The joint velocity is mainly determined by the gain of the trajectory planning algorithm.Through the optimization of the potential field function and use of weighted joint velocities,the joint speed norms can be reduced under the precondition of avoiding joint restriction.Thus,a larger gain can be selected to help the system achieve a better steady-state performance.The Monte Carlo method was used to establish the relationship between the maximum joint speed and gain,which is necessary to determine the gain range for selecting an appropriate gain.The correctness and effectiveness of the algorithm can be proved by selecting different gains in point-topoint and trajectory tracking motion.The study also introduces velocity feedforward in trajectory tracking motion and proves the stability of the two motion formal algorithms by the Lyapunov stability theorem.Results of a simulation verification of the hyper-redundant manipulator independently designed and manufactured by our laboratory revealed that the end position deviation and attitude deviation were less than 10~(-4)mm and 1×10~(-5)rad,respectively,based on the premise of ensuring rapid point-to-point movement.In addition,the trajectory tracking movement position deviation and altitude deviation were less than 10~(-3)mm and 1×10~(-4)rad,respectively.Finally,experimental verification revealed that although the trajectory deviation in the experimental process increased by an order of magnitude compared to the simulation,the requirements of the experimental task were still met.
引文
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[17]PIETRO F,CIRO N.On the stability of closedloop inverse kinematics algorithms for redundant robots[J].IEEE Transactions on Robotics,2011,27(4):780-784.
[2]ISIAH Z,LUIS B.A novel closed-form solution for the inverse kinematics of redundant manipulators through workspace analysis[J].Mechanism and Machine Theory,2018,121:829-843.
[3]CARLOS F,FLORA F,WOLFRAM E,et al..Position-based kinematics for 7-DoF serial manipulators with global configuration control,joint limit and singularity avoidance[J].Mechanism and Machine Theory,2018,121:317-334.
[4]ZHANG Y N,WANG J,XIA Y S.A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits[J].IEEE Transactons on Neural Networks,2003,14(3):658-667.
[5]LUO X P,WEI W.A new immune genetic algorithm and its application in redundant manipulator path planning[J].Journal of Field Robotics,2010,21(3):141-151.
[6]欧群文,贠超,杨学兵,等.基于神经网络的冗余机械臂运动学逆解研究[J].机电工程,2016,33(6):663-667.OU Q W,YUN CH,YANG X B,et al..Algorithm based on neural network for inverse kinematics of redundant manipulator[J].Journal of Mechanical&Electrical Engineering,2016,33(6):663-667.(in Chinese)
[7]GUO D S,XU F,YAN L C.New pseudoinversebased path-planning scheme with PID characteristic for redundant robot manipulators in the presence of noise[J].IEEE Transactions on Control Systems Technology,2017:1-12.
[8]YAZDANI M,NOVIN R S,MASOULEH M T,et al..An experimental study on the failure tolerant control of a redundant planar serial manipulator via pseudo-inverse approach[C].Rsi International Conference on Robotics and Mechatronics.IEEE,2015:365-370.
[9]WAN J,WU H T,MA R,et al..A study on avoiding joint limits for inverse kinematics of redundant manipulators using improved clamping weighted least-norm method[J].Journal of Mechanical Science&Technology,2018,32(3):1367-1378.
[10]KUMAR S,SUKAVANAM N,BALASUBRA-MANIAN R.Anoptimization approach to solve the inverse kinematics of redundant manipulator[J].International Journal of Information and Systems Sciences,2010,6(4):414-423.
[11]黄水华.多约束下的机械臂运动控制算法研究[D].杭州:浙江大学,2016.HUANG SH H.Research on Kinematic Control of Manipulator with Multiple Constraints[D].Hangzhou:Zhejiang University,2016.(in Chinese)
[12]朱明超,刘慧,张鑫,等.惯性稳定平台自适应前馈控制[J].光学精密工程,2015,23(1):141-148.ZHU M CH,LIU H,ZHANG X,et al..Adaptive feed-forward control for inertially stabilized platform[J].Opt.Precision Eng.,2015,23(1):141-148.(in Chinese)
[13]MARK W S,SETH H,VIDYASAGAR M.Robot Modeling and Control[M].John Wiley&Sons Inc,1989.
[14]PETER C.Robotics,Vision and Control[M].Springer International Publishing,2017.
[15]谭民,徐德,侯增广,等.先进机器人控制[M].北京:高等教出版社,2006.TAN M,XU D,HOU Z G,et al..Advanced Robot Control[M].Beijing:Higher Education Press,2006.(in Chinese)
[16]BUSS S R.Introduction to inverse kinematics with jacobian transpose,pseudoinverse and damped least squares methods[J].IEEE Journal of Robotics and Automation,2004,17(16):1-19.
[17]PIETRO F,CIRO N.On the stability of closedloop inverse kinematics algorithms for redundant robots[J].IEEE Transactions on Robotics,2011,27(4):780-784.
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