Numerical methods for the optimal control of constrained mechanical systems

约束机械系统最优控制的数值方法

• 批准号: 442997215
• 负责人: Professor Dr.-Ing. Peter Betsch
• 金额: --
• 依托单位: Institut für Mechanik (IFM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/442997215?language=en
• 关键词: Numerical; methods; optimal; control; constrained

Optimal control problems have many interesting applications in the field of multibody dynamics ranging from the energy efficient control of lightweight robots to the biomechanics of human motion. Provided that minimal coordinates can be found for the description of the multibody system, the equations of motion assume the form of ordinary differential equations which play the role of state equations in the optimal control problem. For this case well-established numerical methods can be applied to solve the optimal control problem. However, the use of minimal coordinates is confined to comparatively simple multibody systems with tree structure. The general approach to multibody dynamics relies on the use of redundant coordinates. Correspondingly, the state equations of the optimal control problem now assume the form of differential-algebraic equations. For this class of problems there is still great need for research, since the common approach does not guarantee that the correct necessary optimality conditions are solved. The goal of the present proposal is the development of new methods which resolve this shortcoming of existing methods.

最优控制问题在多体动力学领域有许多有趣的应用，从轻型机器人的节能控制到人类运动的生物力学。在能够找到描述多体系统的最小坐标的情况下，运动方程采用常微分方程组的形式，在最优控制问题中起到状态方程的作用。对于这种情况，可以用成熟的数值方法来求解最优控制问题。然而，最小坐标的使用仅限于树形结构的相对简单的多体系统。多体动力学的一般方法依赖于使用冗余坐标。相应地，最优控制问题的状态方程现在采用微分-代数方程的形式。对于这类问题，仍然有很大的研究需要，因为通常的方法不能保证正确的必要条件得到解决。本提案的目标是开发新的方法，以解决现有方法的这一缺点。