Model Predictive Control for Nonlinear Mechanical Systems

9813099本研究项目涉及使用反馈控制器为包括机器人和宇宙飞船在内的各种完全和欠驱动机械系统开发路径规划方法。当信息不完全时，所提出的方案能够保证闭环系统的渐近稳定性。此外，通过使用内部惩罚函数，该算法还可以处理不等式约束。这种反馈控制律可以看作是一类特殊的模型预测控制(MPC)，因为每个时刻的控制动作都是基于未来轨迹来确定的。然而，与需要在每个控制时间间隔解决优化问题的标准MPC方案相比，只需要计算一个牛顿步长，涉及到固定的计算量。该算法的有效性已经在许多困难的例子中得到了验证，包括轮式车辆的运动控制、欠驱动六自由度卫星的稳定以及欠驱动机械手的稳定。提出的研究重点包括：i)在算法中建立保证闭环系统稳定的参数选择规则；ii)量化由于模型缺陷和外部扰动引起的向量场扰动时的稳定性鲁棒裕度；iii)通过参数自适应来增强鲁棒性；iv)利用梯度算子中的零空间来避免奇点和处理约束；v)发展控制计算中选择逼近基的策略，并分析逼近对收敛的影响；vi)应用于大量涉及非线性机械系统的实验。***

9813099 Wen This research project deals with the development of path planning methods using a feedback controller for a variety of fully and under-actuated mechanical systems, including robots and spacecrafts. The proposed scheme can guarantee the closed-loop asymptotic stability when information is imperfect. Furthermore, by using interior penalty functions, inequality constraints can also be handled by the algorithm. This type of feedback control law can be considered as a special class of model predictive control (MPC), since the control action at each time instance is determined based on the future trajectory. However, in contrast with the standard MPC schemes where an optimization problem needs to be solved at each control time interval, only one Newton step needs to be computed involving a fixed amount of computation. The efficacy of this algorithm has been demonstrated on a number of difficult examples, including the kinematic control of wheeled vehicles, stabilization of underactuated 6-DOF satellites, and stabilization of underactuated manipulators. The key research thrusts in the proposed research include: i)develop parameter selection rule in the algorithm that will grarantee closed loop stability; ii) quantify the stability robustness margin when the vector field is perturbed due to model imperfection and external disturbances; iii)enhance robustness through parameter adaptation; iv)utilize null space in the gradient operator for singularity avoidance and constraint handling; v)develop stategies for choosing the approximation basis in control computation and analyze the effect of approximation on convergences, and vi) apply to a number of experiments involving nonlinear mechanical systems. ***