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<p>This paper studies a computationally efficient and robust method for path planning and path following tasks for unmanned systems. The method is based on relaxed differential-algebraic equations (DAEs), which allow to handle deviations from a prescribed path. The relaxation is designed by a suitably formulated optimal control problem with the aim to guide the system back to the desired path in a smooth way. The approach merely requires to solve a higher index DAE numerically. In addition, a parametric sensitivity analysis can be used to obtain Taylor approximations of perturbed solutions at very low computational cost. We demonstrate the method for a path following task with an unmanned ground vehicle (UGV) and a transition to hover maneuver of an unmanned aerial vehicle (UAV).</p>

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Relaxed DAEs in path planning and path following

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月24日

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  • Felix Mitze,
  • Matthias Gerdts

摘要

This paper studies a computationally efficient and robust method for path planning and path following tasks for unmanned systems. The method is based on relaxed differential-algebraic equations (DAEs), which allow to handle deviations from a prescribed path. The relaxation is designed by a suitably formulated optimal control problem with the aim to guide the system back to the desired path in a smooth way. The approach merely requires to solve a higher index DAE numerically. In addition, a parametric sensitivity analysis can be used to obtain Taylor approximations of perturbed solutions at very low computational cost. We demonstrate the method for a path following task with an unmanned ground vehicle (UGV) and a transition to hover maneuver of an unmanned aerial vehicle (UAV).