Position synchronization of multiple motion axes with adaptive coupling control.
With the ever increasing demand for greater productivity the robots more and more widely uses in the modern manufacturing. The next step in the automation of the manufacturing is the employment of integrated robots with the intersecting operation space i.e., when individual operations are combined into one operation. The example of such integrated robot cell containing four planar manipulators is considered in the represented paper. The problem of workability satisfaction of such cross-coupling technology robot-cell is synchronization of movement of every manipulator which excludes the intersecting of their trajectories. In the considering case the problem is reduced to adaptive coupling control for position synchronization of multiple motion axes. And in such statement the mentioned problem is very difficult and challenger. Strategy of multi-axis synchronization considers a motion control system with \(n\) axis the dynamics which are described by the system of ordinary differential equations of the second-order with variable inertia and damping and other nonlinear unexpected disturbances. The position tracking error of the \(i\)th axis is defined as \(e_i(t)= x^d_i(t)- x_i(t)\), where \(x^d_i(t)\) denotes the desired position of the \(i\)th axis, \(x_i(t)\) are the its coordinates in the real motion. The main control goal of synchronized motion \(e_i(t)\to 0\) simultaneously may be treated like demand \(e_1(t)= e_2(t)=\cdots= e_n(t)\). So the main goal may be divided into \(n\) sub-goals of all position pairs of two axes synchronization errors in the following way: \[ \varepsilon_1(t)= e_1(t)- e_2(t);\, \varepsilon_2(t)= e_2(t)- e_3(t);\dots; \varepsilon_n(t)= e_n(t)- e_1(t) \] and if \(\varepsilon_i(t)= 0\), for all \(i\), the goal of multi-axis synchronization can be achieved. Including the new variables, named coupled position error by means following expression \[ e^*_i(t)= e_i(t)+ \beta \int^e_0 (e_i(w)- e_{i-1}(w))\,dw, \] where \(\beta\) is a positive coupling parameter, and defining the command vectors \[ u_i(t)= x^d_i(t)+ \beta(\varepsilon_i(t)- \varepsilon_{i-1}(t))+ \Lambda e^*_i(t), \] \(\Lambda\) positive number, was formed the positive-definite Lyapunov function with negative-definite derivative, which guarantee the asymptotic stability of the designed controller, when converges to zero both the position errors and synchronization errors. Simulation of multi-axes motion control system confirms the effectiveness of the elaborated method.
position synchronization of multiple axes
scientific article; zbMATH DE number 1924703