Real-Time Model Predictive Control of Rigid Body Motion via Discretization Using the Cayley Map
Real-Time Model Predictive Control of Rigid Body Motion via Discretization Using the Cayley Map
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DOI：
10.1109/access.2020.2966240
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发表时间：
2020-01
期刊：
影响因子：
3.9
通讯作者：
Yuichi Tadokoro;Yuki Taya;Tatsuya Ibuki;M. Sampei
中科院分区：
文献类型：
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作者：
Yuichi Tadokoro;Yuki Taya;Tatsuya Ibuki;M. Sampei
本文提出了一种基于特殊欧几里德群SE(3)的航天器或飞行器等刚体动力系统的快速非线性模型预测控制方法。本研究的重点是在低成本的嵌入式计算机上实现最优控制的实时执行。刚体的位置和方向通过SE(3)的Cayley映射表示为6维矢量。基于该表示，运动可以精确地离散到代数se(3)上。因此，可以选择粗采样间隔来减少预测步数。在此基础上，应用递归离散化技术，通过消除非线性优化问题中的状态，有效地减少了决策变量。在树莓派单板计算机上的仿真结果证明了该模型预测控制方法的实时可行性。在全驱动六旋翼无人机上的实验进一步验证了该控制器的有效性。
This paper presents a fast nonlinear model predictive control method for rigid body dynamical systems such as spacecraft or aerial vehicles on the special Euclidean group SE(3). The focus of this research is on the real-time execution of the optimal control on a low-cost embedded computer. The position and orientation of a rigid body are expressed as a 6-dimensional vector via the Cayley map for SE(3). Based on the representation, the motion can be exactly discretized on the algebra se(3). As a result, coarse sampling intervals can be selected to reduce the number of prediction steps. Furthermore, the recursive discretization technique is applied to effectively reduce the decision variables of the nonlinear optimization problem by eliminating states from them. Simulation results on a Raspberry Pi single-board computer are given to prove that the present model predictive control method is feasible in real time. The effectiveness of the present controller is further verified by an experiment using a fully actuated hexarotor unmanned aerial vehicle.