Holonomic (robotics)

A robot is holonomic if all the constraints that it is subjected to are integrable into positional constraints of the form

The variables ${\displaystyle q_{i}}$ are the system coordinates. When a system contains constraints that cannot be written in this form, it is to be nonholonomic.

Consider a mobile robot such as the one depicted to the right, moving in the two-dimensional plane. Imagine that three omnidirectional wheels are mounted on the frame of the robot. Each wheel ${\displaystyle W_{i}}$ is described by its coordinates ${\displaystyle (x_{i},y_{i})}$, so that a configuration of the robot can be given by the six scalars ${\displaystyle (x_{1},y_{1},x_{2},y_{2},x_{3},y_{3})}$. Also, each wheel ${\displaystyle W_{i}}$ can impulse a velocity ${\displaystyle \mathbf {v} _{i}=(v_{x,i},v_{y,i})}$ to the robot. However, because all three wheels are connected by the rigid robot frame, their relative velocities are zero (unless the frame breaks):

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