用克拉克变换构建连续机器人控制框架，实现高效平滑轨迹生成。
Using Clarke Transform to Create a Framework on the Manifold: From Sampling via Trajectory Generation to Control
- 基于克拉克坐标在流形上构建规划、轨迹生成与控制模块。
- 四段式连续机器人仿真中实现平滑轨迹与约束满足。
- 适合需要高精度轨迹控制的柔性机器人研究者使用。
我们提出一种基于克拉克坐标的空间位移驱动连续机器人控制框架，适用于任意节数的机器人。该框架由三个模块化组件构成：规划器、轨迹生成器和控制器，均定义在流形上。所有组件计算高效、结构紧凑且无分支。可通过编码器接入不基于克拉克坐标的现有组件。推导了关节空间运动学约束与流形上轨迹之间的关系，以生成流形上的平滑轨迹。进一步建立了位移约束与平行曲线之间的关联。通过一个四段式位移驱动连续机器人的仿真演示，验证了框架的有效性。
原文摘要 · Abstract (English)
We present a framework based on Clarke coordinates for spatial displacement-actuated continuum robots with an arbitrary number of joints. This framework consists of three modular components, i.e., a planner, trajectory generator, and controller defined on the manifold. All components are computationally efficient, compact, and branchless, and an encoder can be used to interface existing framework components that are not based on Clarke coordinates. We derive the relationship between the kinematic constraints in the joint space and on the manifold to generate smooth trajectories on the manifold. Furthermore, we establish the connection between the displacement constraint and parallel curves. To demonstrate its effectiveness, a demonstration in simulation for a displacement-actuated continuum robot with four segments is presented.
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