Efficient Online Trajectory Planning for Integrator Chain Dynamics Using Polynomial Elimination

Providing smooth reference trajectories can effectively increase performance and accuracy of tracking control applications while overshoot unwanted vibrations are reduced. Trajectory planning computations often be simplified significantly by transforming the system dynamics into decoupled integrator chains using methods such as feedback linearization, differential flatness or Brunovsky normal form. We present an efficient method to plan for subject derivative bound constraints. Therefore, algebraic precomputation algorithm formulates necessary conditions time optimality in form a set polynomial systems, followed symbolic elimination Gröbner bases. A fast online then plans calculating roots decomposed systems. These describe switching instants input signal full trajectory simply follows multiple integration. This presents systematic way compute fast, low orders even optimal exactly via calculations without numerical approximation iterations. It is applied various types with different continuity order, asymmetric bounds non-rest initial final states.