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How do I control a double pendulum to get the end effector link to go in the trajectory shaped in a perfect circle?

I have the equation of the circle to go in but I don't know how to get the double pendulum links to move in on that planned trajectory. What steps should I take?

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closed as too broad by CroCo, sempaiscuba, holmeski, Greenonline, Peter Corke Apr 13 at 1:26

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  • $\begingroup$ Which actuators do you have, i.e. can you apply a torque at each joint? And how big is the circle, is it small enough so that you could still use a linearized model? $\endgroup$ – fibonatic Mar 7 at 7:43
  • $\begingroup$ In the literature the term “tracking control” is used for doing the task. Tracking means, that the double pendulum has to follow the circle, while control is referencing to model predictive control. The task itself isn't a trivial one. Some projects were made in the past around the Matlab/Simulink ecosystem. $\endgroup$ – Manuel Rodriguez Mar 7 at 11:49
  • $\begingroup$ @fibonatic No torque on the joints. Just a simple 2-link model. The circle is small. $\endgroup$ – user22378 Mar 20 at 9:01
  • $\begingroup$ @ManuelRodriguez Yes I want the end effector to follow the trajectory of the circle using control equations if possible. Do you have any suggestions for how to complete this? $\endgroup$ – user22378 Mar 20 at 9:02
  • $\begingroup$ You can't apply control if you do not have any input signals. $\endgroup$ – fibonatic Mar 20 at 10:17
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If I understand correctly, this is a double pendulum.

enter image description here

This is a 2-DOF simple kinematic chain so trying make it go along a trajectory, shouldn't be really difficult. You can get analytical solutions to inverse kinematics for this and easily solve the IK at each timestep. This would get you the desired joint angles for the same and you can actuate your joints accordingly.

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