采用预测控制的龙门架式冗余自由度机械臂轨迹规划算法
The trajectory planning of redundant manipulator with gantry by using model predictive control

为解决近年来工业常用的复杂结构大型机械臂的运动控制问题, 本文以龙门架式机械臂为研究对象, 首先 结合材料力学分析, 对在双臂荷载下的横梁挠度公式进行推导, 进而对机械臂系统建立精确的运动学模型. 为了便 于后期算法设计, 又在此基础上进行了降阶、线性化等模型简化工作. 针对这一具有关节限位等约束条件和冗余自 由度的多输入多输出高维复杂系统, 提出了一种基于预测控制的轨迹规划算法. 该算法根据模型中不同关节的运 动范围以及定位精度等特性, 划定其不同的运动优先级, 通过在优化问题中对各个关节控制量设置不同的权重, 来 解决冗余问题. 同时通过实时更新与滚动优化, 很好的保证了控制的及时性. 仿真结果表明了本文所推导的挠度公 式的准确性和所提出算法的有效性, 不仅很好地解决了冗余问题, 而且充分利用不同关节的运动特性, 针对不同类 型的跟踪目标值给出相适应的轨迹规划方案.
To solve the motion control problem of large-scale complex manipulators which are commonly used in industry recently, this paper focuses on manipulator system composed of a gantry and small-sized manipulators. Firstly the calculation formula for beam deflection under two independent concentrated loads is deduced by analyzing material mechanics. Then an accurate kinematics model of manipulator system is presented. On this basis, the model is simplified to be linear and low-order, for following algorithm design. For the multi-input multi-output (MIMO) high dimensional redundant model with joint constraints, an algorithm based on model predictive control (MPC) is proposed for trajectory planning. All of the joints are classified into different movement priorities according to their motion range and positioning accuracy. The redundancy problem can be solved by setting different weights for control variable of each joint in optimization problem. Meanwhile, rolling optimization style of MPC scheme makes it possible to online continuously make trajectory planning with updated information. The simulation results illustrate effectiveness of the algorithm proposed in this paper. In addition, for various setting points, different weighting selections are considered by analyzing joints’ motion characteristics.