Abstract This paper presents a dynamic transition trajectory planning technique for fully-actuated three-degree-of-freedom cable-suspended parallel robots. The proposed two-step technique can be used to plan transition trajectories to general periodic motions that extend beyond the static workspace of the mechanism. In the first step, the robot dynamics are linearized and partly decoupled by handling the less restricted gravity axis trajectory planning problem. The corresponding dynamic model and constraints of the other axes then become linear time-varying. Secondly, the generation of general periodic trajectories and the general transition trajectories is accomplished by convex optimization. The formulation of a constrained linear-quadratic optimal control problem for the dynamic transition task shows essential differences from previous works and extends to general cases. The proposed technique has the ability to generate general periodic trajectories and provides a universal transition planner. Indeed, there is no need to rely on a specific amplitude increment function, which makes the planning technique more flexible and applicable to general cases. Moreover, the quadratic programming problems can be solved reliably and rapidly. Example transition trajectories to harmonic and to non-harmonic periodic trajectories are given in order to illustrate the approach.

中文翻译：

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基于线性时变MPC的三自由度悬索并联机器人动态过渡轨迹规划

摘要 本文提出了一种全驱动三自由度悬索并联机器人的动态过渡轨迹规划技术。所提出的两步法可用于规划过渡轨迹到超出机构静态工作空间的一般周期性运动。第一步，机器人动力学被线性化并通过处理较少限制的重力轴轨迹规划问题部分解耦。相应的动态模型和其他轴的约束随后变为线性时变。其次，一般周期轨迹和一般过渡轨迹的生成是通过凸优化完成的。动态转换任务的约束线性二次最优控制问题的公式显示出与以前工作的本质区别，并扩展到一般情况。所提出的技术具有生成一般周期性轨迹的能力，并提供了一个通用的过渡规划器。实际上，不需要依赖特定的幅度增量函数，这使得规划技术更加灵活并且适用于一般情况。此外，二次规划问题可以可靠快速地解决。为了说明该方法，给出了到谐波和非谐波周期性轨迹的示例过渡轨迹。不需要依赖特定的幅度增量函数，这使得规划技术更加灵活，适用于一般情况。此外，二次规划问题可以可靠快速地解决。为了说明该方法，给出了到谐波和非谐波周期性轨迹的示例过渡轨迹。不需要依赖特定的幅度增量函数，这使得规划技术更加灵活，适用于一般情况。此外，二次规划问题可以可靠快速地解决。为了说明该方法，给出了到谐波和非谐波周期性轨迹的示例过渡轨迹。