Question

一个单连杆转动关节机器人静止在关节角 $\theta=-5^{\circ}$ 处。希望在 4 秒内平滑地将关节转动到 $\theta=$ $80^{\circ}$ 并平滑地停止。求出带有抛物线过渡的直线轨进的相应参数。画出位置、速度和加速度的时间函数。

   一个单连杆转动关节机器人静止在关节角 $\theta=-5^{\circ}$ 处。希望在 4 秒内平滑地将关节转动到 $\theta=$ $80^{\circ}$ 并平滑地停止。求出带有抛物线过渡的直线轨进的相应参数。画出位置、速度和加速度的时间函数。
机器人学导论 introduction to robotics: mechanics and control
机器人学导论 introduction to robotics: mechanics and control
约翰 J.克雷格 4th Edition
Chapter 7, Problem 3 ↓

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However, the question specifies a parabolic transition, which suggests using a motion profile that includes quadratic (parabolic) segments for acceleration and deceleration. This can be achieved using a quintic polynomial for position, which ensures smooth  Show more…

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一个单连杆转动关节机器人静止在关节角 $\theta=-5^{\circ}$ 处。希望在 4 秒内平滑地将关节转动到 $\theta=$ $80^{\circ}$ 并平滑地停止。求出带有抛物线过渡的直线轨进的相应参数。画出位置、速度和加速度的时间函数。
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