Real-time capable model inversion of underactuated multibody systems using servo-constraints

使用伺服约束对欠驱动多体系统进行实时模型反演

• 批准号: 396289190
• 负责人: Professor Dr.-Ing. Robert Seifried
• 金额: --
• 依托单位: Institut für Mechanik und Meerestechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/396289190?language=en
• 关键词: Real; time; capable; model; inversion

Underactuated multibody systems are mechanical systems which haves less control inputs than degrees of freedom. An inverse model provides for a given output trajectory the associated control inputs and the trajectories of all coordinates of the system. Inverse models are used as feedforward control in combination with feedback control for trajectory tracking of multibody systems. The aim of the proposed project is the development of real-time capable inverse models of underactuated multibody systems. Thereby the servo-constraint approach is used, which originates in multibody dynamics. This is a systematic numerical approach which is applicable to a wide range of systems. The mathematical model of multibody systems consists of the equation of motion with control inputs and the defined output equations. For the inverse model additional servo-constraints for the output are defined, such that these follow predefined trajectories. The systems considered in this project are either differentially flat systems or systems with stable internal dynamics. The biggest challenge in this project is the design and real-time solution of inverse models, which have a higher differential index and an internal dynamics. At the end of this project such systems should be treated, especially with several inputs and outputs. In the scope of this project it should also be investigated if the choice of coordinates, i.e minimal coordinates or redundant coordinates, has an influence on the solution and efficiency of the inverse model. Currently this is an open question since due to the servo-constraints always a differential algebraic equation arises. Using the simple example of a crane it has been already demonstrated that here redundant coordinates are not necessarily less efficient than using generalized coordinates. This will be especially interesting for more complex three-dimensional systems. Under given time step constraints the limits of real-time capable model inversion should be tested. Hereby for systems with internal dynamics it has to be considered that their characteristic might be fundamental faster than the forward dynamics. Finally, using basic experiments the accuracy of inverse models should be tested. Therefore a modular testbed will be set-up, which allows the testing of 4 structurally different systems.

欠驱动多体系统是指控制输入小于自由度的机械系统。逆模型为给定的输出轨迹提供相关的控制输入和系统的所有坐标的轨迹。将逆模型作为前馈控制与反馈控制相结合，用于多体系统的轨迹跟踪。该项目的目的是开发实时欠驱动多体系统的逆模型。因此，伺服约束的方法，这起源于多体动力学。这是一个系统的数值方法，适用于广泛的系统。多体系统的数学模型由具有控制输入的运动方程和定义的输出方程组成。对于逆模型，定义用于输出的附加伺服约束，使得这些伺服约束遵循预定义的轨迹。在这个项目中考虑的系统是微分平坦系统或系统具有稳定的内部动态。该项目的最大挑战是具有较高微分指数和内部动态特性的逆模型的设计和实时求解。在本项目结束时，应处理此类系统，特别是具有多个输入和输出的系统。在本项目的范围内，还应调查坐标的选择，即最小坐标或冗余坐标，是否对逆模型的解和效率有影响。目前，这是一个悬而未决的问题，因为由于伺服约束总是一个微分代数方程出现。使用起重机的简单示例已经证明，这里冗余坐标不一定比使用广义坐标效率低。这对于更复杂的三维系统尤其有趣。在给定的时间步长约束条件下，应测试实时模型反演的极限。因此，对于具有内部动态的系统，必须考虑它们的特性可能比前向动态快。最后，利用基础实验对反演模型的精度进行检验。 因此，将建立一个模块化测试平台，允许测试4个结构不同的系统。