Abstract
For the 6R robot, there is no analytical solution for some configurations, so it is necessary to analyse inverse kinematics (IK) by the general solution method, which cannot achieve high precision and high speed as the analytical solution. With the expansion of application fields and the complexity of application scenarios, some robots with special configuration have become the research hotspot, and more high-speed and high-precision general algorithms are still being explored and studied. The present paper optimized two general solutions. Elimination is a numerical solution, which has high accuracy, but the solution process is complex and time-consuming. The present paper optimized the elimination method, derived the final matrix expression directly through complex coefficient extraction and simplifying operation, and realized one-step solution. The solving speed was reduced to 15% of the original, and the integrity of the method was supplemented. This paper proposed a new optimization method for the Gaussian damped least-squares method, in which the variable step-size coefficient is introduced and the machine learning method is used for the research. It was proved that, on the basis of guaranteeing the stability of motion, the average number of iterations can be effectively reduced and was only 4-5 times, effectively improving the solving speed.
Highlights
For 6R robots, most configurations satisfy the Pieper criterion; that is, the adjacent three axes are parallel or intersect at one point, and there is analytical solution, which can be solved with high speed and high precision
A neural-network committee machine (NNCM) is designed in [24] to solve the inverse kinematics of a 6R redundant manipulator to improve the precision of the solution
When the robot is close to the singular configuration, the minimum singular value is approximate to 0 and joint speed is infinitely great, which is the reason why the pseudoinverse method is unstable. e damped least-squares (DLS) method incorporates the damping factor λ on this basis to minimize X_ − Jθ_ 2 + λ2θ_ ∗2, and as a result, as the robot approaches the singular configuration, the solving accuracy and joint speed are balanced, and the joint speed is θ_ ∗
Summary
For 6R robots, most configurations satisfy the Pieper criterion; that is, the adjacent three axes are parallel or intersect at one point, and there is analytical solution, which can be solved with high speed and high precision. Is paper optimized the elimination method to improve the solving speed and make the algorithm more complete. There are three main categories of algorithms: iterative algorithm, numerical and geometric methods, and soft computing methods. A generalized solution for a subproblem of inverse kinematics based on an exponential formula product is proposed in [16]. A comparative study between different soft computing-based methods (artificial neural network, adaptive neuro-fuzzy inference system, and genetic algorithms) applied to the problem of inverse kinematics is presented in [19]. A neural-network committee machine (NNCM) is designed in [24] to solve the inverse kinematics of a 6R redundant manipulator to improve the precision of the solution. An approach for solving the inverse kinematics of manipulator robots based on soft computing algorithms is introduced in [25]. Each decision tree is obtained by using all training samples, and the bifurcation values are obtained completely randomly
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