This paper proposes a model-based approach to control the shape of a tensegrity system by driving its node position locations. The nonlinear dynamics of the tensegrity system is used to regulate position, velocity, and acceleration to the specified reference trajectory. State feedback control design is used to obtain the solution for the control variable as a linear programming problem. Shape control for the gyroscopic tensegrity systems is discussed, and it is observed that these systems increase the reachable space for the structure by providing independent control over certain rotational degrees of freedom. Disturbance rejection of the tensegrity system is further studied in the paper. A methodology to calculate the control gains to bound the errors for five different types of problems is provided. The formulation uses a Linear Matrix Inequality (LMI) approach to stipulate the desired performance bounds on the error for $\mathcal{H}_\infty$, generalized $\mathcal{H}_2$, LQR, covariance control and stabilizing control problem. A high degree of freedom tensegrity $T_2D_1$ robotic arm is used as an example to show the efficacy of the formulation.
翻译:本文提出一种基于模型的方法,通过驱动其节点位置来控制时态系统形状。 时态系统的非线性动态用于调节位置、 速度和加速到指定的参考轨迹。 国家反馈控制设计用于作为线性编程问题获得控制变量的解决方案。 讨论对陀螺色时态系统的形状控制,并观察到这些系统通过对某些旋转自由度提供独立控制来增加结构的可达空间。 文件中进一步研究了对时态系统的扰动拒绝。 提供了一种计算控制收益以约束五种不同类型问题的错误的方法。 配方使用线性矩阵不平等(LMI)方法来规定对 $\mathcal{H ⁇ }H ⁇ infty$、 通用 $\mathcal{H ⁇ 2$、 LQR、 软性控制和稳定控制问题。 高度的自由性紧张 $T_ 2D_ 1$ 机器人臂是用来显示配制效力的一个例子。