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Does the robot described by Double Integrator Model is holonomic ?

Let's say we have a robot with dynamics described by equations

\begin{cases} \dot x = v, & \\ \dot v = \frac {1}{m}u \end{cases} Where, $x$ is the position of the robot, $v$ is the velocity and $u$ is robot's control input.

Can we call this robot a holonomic robot ?

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  • $\begingroup$ This question was multi-posted to physics.se. $\endgroup$
    – Mark Booth
    Jul 2 '17 at 20:49
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A holonomic robot is one where the number of degrees of freedom is equal to the number of controllable axes.

In your case, you are controlling acceleration (one axis of control) but there is also only one degree of freedom - position. So, the robot is holonomic.

An example of a non-holonomic robot would be a differentially steered robot, like a micro mouse or a tank. There you can only control the left and right wheel speeds, but you can move to any x/y position AND you can be at any position with any heading. You can control two things, but the vehicle can move in three ways - forward/backward, rotate, and then left and right by rotating, driving forward, then rotating again.

Similarly, an Ackerman steered vehicle is also non-holonomic. There you can only control speed and steering angle, but again you can arrive at any x/y position with any heading. Again, two axes of control but three degrees of freedom.

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