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 $\theta=$ $80^{\circ}$ 。求出完成此运动并且使目标停在目标点的三次曲线的系数。画出位华、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 $\theta=$ $80^{\circ}$ 。求出完成此运动并且使目标停在目标点的三次曲线的系数。画出位华、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 2 ↓

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We want to find a cubic polynomial $\theta(t) = at^3 + bt^2 + ct + d$ that describes the motion of the joint from $\theta(-5^\circ)$ to $\theta(80^\circ)$ over 4 seconds. Here, $t$ is the time in seconds. Step 2: Set up boundary conditions. We need to set  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 $\theta=$ $80^{\circ}$ 。求出完成此运动并且使目标停在目标点的三次曲线的系数。画出位华、速度和加速度的时间函数。
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