In this paper, a third-order S-curve is used to model the motion issue. A closed method of solving is derived for the optimal point-to-point(P2P) time issue based on the model. Based on the P2P time-optimal solution, a closed multi-axis synchronization algorithm (MASA) method is proposed. This method considers the kinematic equation of the S-curve based on the inverse function of the multivariate function. Therefore, the inverse function of the execution time is derived via the kinematic equation of the P2P time optimization issue and solving a set of smaller bandwidth parameters is an important attempt in this paper. Otherwise, based on the MASA proposed in this paper, a synchronous computing framework suitable for the planning of robot space poses was designed. This framework can effectively solve problems with robot pose planning. The innovations of this article can be summarized as:(1)Based on the third-order S-curve, this paper deduced a complete method for solving the P2P time-optimal curve.(2) Based on the method for solving the time-optimal curve, this paper further derived three synchronization methods based on time constraints.(3) Based on the MASA proposed in this paper, a synchronous computing framework suitable for the planning of robot space poses was designed. The continuity and smoothness of the robot joint spatial motion can be guaranteed in the Descartes space. Few scholars have studied the closed solution method of multi-axis synchronization. The research in this paper promotes the theoretical research of motion control.
This study proposes a method for judging the existence of closed-form inverse kinematics solutions based on the Denavit–Hartenberg (DH) model. In this method, serial robots with closed-form solutions are described using three types of sub-problems from the viewpoint of solving algebraic equations. If a serial robot can be described using these three types of sub-problems, i.e., if the inverse kinematics problems can be solved by several basic problems, then there is a closed-form solution. Based on the above method, we design a set of universal closed-form inverse kinematics solving algorithms. Since there is a definite formula solution for the three types of sub-problems, the joint angles can be rapidly determined. In addition, because the DH parameters can directly reflect the linkage of the robot, the judgment of the sub-problems is also quick and accurate. More importantly, the algorithm can be applied to serial robots with low degrees of freedom. This enables the algorithm to not only quickly and accurately solve inverse kinematics problems but also to exhibit high universality. This proposed theory improves the existence conditions for closed-form reverse solutions and further promotes the development of motion control techniques for serial robots.
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