Analytical Multi-Point Trajectory Generation for Differentially Flat Systems with Output Constraints

Abstract: In this paper, an analytical off-line multi-point trajectory generation scheme is presented for differentially flat systems. For control of dynamical systems along a given set of control points, multi-point trajectory generation is required when input and state constraints exist. It is assumed that differential constraints for flat coordinates can be formulated explicitly. The trajectory scheme is based on analytically solving a set of polynomial equations to parameterize n-times continuously differentiable segmented transition polynomials, that approximate time optimal trajectories. The computational effort for determining valid trajectories is low in comparison to numerical optimization. As an example, a multi-point trajectory generation problem for a 3-DOF gantry crane is presented