I'm new to robotics and I've been reading some slides online regarding motion planning. Due to my lack of knowledge in mechanical engineering, I'm having a difficult time understanding what holonomic and non-holonomic constraints mean.

I saw a post here and it says Holonomic system is when a robot can move in any direction in the configuration space, and Nonholonomic systems are systems where the velocities (magnitude and or direction) and other derivatives of the position are constraint.

It seems like holonomic system differs from holonomic constraint. What is holonomic constraint and when do we need it? What is non-holonomic constraint and when do we need that?

Thanks in advance.


1 Answer 1


A constraint on the $k$ coordinates $r_1,r_2,...,r_k$ is holonomic if it is an equality constraint of the form $$g(r_1,...,r_k)=0,$$ and nonholonomic otherwise. These sorts of constraints arise frequently in mechanical systems (e.g. when deriving Euler-Lagrange equations of motion). A holonomic system is one that is subject to holonomic constraints, and a nonholonomic system is one that is subject to nonholonomic constraints.

An example of a holonomic system is a sphere on a surface, which can roll in any direction. In contrast, a wheel on a surface without slipping is an example of a non-holonomic system because it cannot roll in any direction--it can only roll forward/backward at some heading.

  • $\begingroup$ I see. What exactly are holonomic and non-holonomic constraints? Do you mind providing an example of those constraints? $\endgroup$
    – MoneyBall
    Commented Apr 14, 2017 at 7:53

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