含不等式约束的欠驱动系统约束跟随控制

在运动控制领域, 欠驱动机械系统通常需要满足一系列的等式约束(完整或非完整的)以便获得较好的运动表现, 同时出于安全考虑还需要满足一定的不等式约束条件. 本文提出了一种约束跟随控制方法, 用以解决同时含等式和不等式约束的欠驱动系统控制问题. 该控制设计主要分为两步: 第1步: 只考虑系统需要满足的等式约束, 运用约束跟随控制方法推导出基于系统模型的状态反馈控制律; 第2步: 考虑系统需要满足的不等式约束, 先通过状态变量映射将不等式约束整合到原等式约束中以得到新的等式约束, 再基于新的等式约束和第1步所述的约束跟随控制方法, 推导出系统所需的状态反馈控制律. 将该约束跟随控制方法应用于三自由度非线性强耦合的欠驱动平面垂直起降(PVTOL)飞行器. 仿真结果表明, 该控制方法能有效处理PVTOL飞行器运动过程中需满足的等式约束(轨迹跟踪和姿态保持)和不等式约束(边界服从).

Constraint-following control for underactuated systems with inequality constraints

In the field of motion control, underactuated mechanical systems are required to obey a set of holonomicand/or nonholonomic equality constraints in order to achieve better performance. On the other hand, due to the safety concerns,they also need to obey some inequality constraints. This paper endeavours to develop a constraint-following controlmethodology to solve the control problems of underactuated systems subject to both equality and inequality constraints.The control is designed in two steps. First, without considering the inequality constraints, constraint-following control designfor underactuated systems is investigated. Second, a variable transformation technique is introduced to incorporate theinequality constraints into the equality constraints, yielding new equality constraints. The new equality constraints includethe original equality constraints and the inequality constraints. Therefore, we are able to obtain the constraint-followingcontrol that renders the system to satisfy the original equality constraints and the inequality constraints, via designing theconstraint-following control rendering the system to follow the new equality constraints based on the first step. The effectivenessof the proposed control is demonstrated on planar vertical take-off and landing (PVTOL) aircraft by numericalsimulation, which has both equality constraints (trajectory tracking and attitude maintaining) and inequality constraints(boundary obedience).