I would like to know the simple difference between kinematic, dynamic and differential constraints in robotic motion planning.

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    $\begingroup$ What you have found already, and what is your current understanding of these concepts? If you provide more information (such as what you already know), it would both make a better question and would generate higher quality answers. $\endgroup$
    – Shahbaz
    Commented Jan 20, 2015 at 10:14

1 Answer 1


Kinematic constraints involves only constraint on the motion (kinematics means the study of motion without considering the force that causes it), which may involve configuration variables and their time derivatives (including higher order derivatives). In particular, no inertial parameters are involved in the constraint. The constraint is geometric in nature, since it restricts the free motion in your configuration space (or state space if there is some constraint on the velocity) to a submanifold defined by the constraints.

If the constraints involve no time derivative of the configuration variables, it is sometimes called a holonomic constraint. Your robot is constrained to move on a submanifold (or a hypersurface if it pleases you). In this case, you have a reduced number of independent configuration variables, or to say the robot has a reduced number of degrees of freedom

If the constraints involve time derivative of the configuration variables, it is called a differential constraint. It is very tricky in this situation, since some differential constraints might actually come from time differentiation of holonomic constraints, in which case we say it is integrable. Integrable differential constraints are in fact holonomic constraints and should be treated as one. Nonintegrable differential constraints are also called nonholonomic constraints. It may or may not reduce the robot's degrees of freedom, depending on certain reachability conditions (similar to a controllability condition).

A dynamic constraint, conceivably, is one involving not only kinematics but also inertias, forces, dampings, stiffness, etc. Usually, up to second order configuration variables are involved (third order may be involved in the case of vibration analysis, trajectory generation, etc).


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