Time Optimal Contouring Control of Industrial Biaxial Gantry: A Highly Efficient Analytical Solution of Trajectory Planning

Contouring control is an important issue in industrial applications. For better product quality and higher productivity, achieving higher contour tracking performance with feed rate as large as possible is essential. However, most existing research has focused on improving contour tracking accuracy only. The potential instability issue due to control input saturation under high feed-rate operations has been largely ignored. In this paper, the minimum time trajectory planning problem is formulated as a step toward solving this practically important problem. A novel back and forward check algorithm is developed to take into account physical constraints of the system when generating the desired trajectory to be followed. Compared with traditional numerical searching methods, the proposed algorithm is very computationally efficient because the optimal solution at each node can be obtained by several analytical equations directly. Moreover, the algorithm can incorporate some velocity-dependent constraints easily. Planning a Lissajous curve is used as the case study to verify the optimality and computational efficiency of the proposed algorithm. Experiments are conducted on an industrial biaxial gantry. Several implementation issues on tracking complicated contours are discussed. Experimental results indicate that the proposed trajectory planning approach enables simultaneous achievement of high contouring tracking accuracy and higher feed rate or shorter operation time.