Coriolis and centrifugal terms
In a multi-joint robot, the Coriolis and centrifugal terms are the extra forces that appear purely because the robot is already moving — forces that vanish the instant it holds still. They are the part of the dynamics driven not by gravity and not by acceleration, but by velocity: how fast the joints are turning right now. Picture a spinning office chair. When you stick your legs out while spinning, you feel a force flinging them outward; that outward fling is the centrifugal effect. And if you move your arms in or out while still spinning, you feel a sideways nudge that wasn't there before; that sideways nudge is the Coriolis effect.
These forces matter because robot joints are linked, so motion in one joint quietly stirs up forces at the others. The centrifugal terms grow with the square of a joint's own speed — spin twice as fast and the outward fling roughly quadruples. The Coriolis terms arise when two joints move at once, coupling their velocities into a force felt elsewhere in the arm. Neither comes from any motor pushing on purpose; both are bookkeeping for the way a moving, jointed body shoves itself around. Engineers often gather them into a single object written C(q,q̇), where the q̇ is a reminder that these forces depend on how fast the joints are moving.
Ignore these terms and a robot moving slowly will behave almost as you expect — but command it to move fast, and the unmodeled velocity forces throw it off course, causing overshoot, drift, or vibration. That is why high-speed, high-precision control must explicitly compute and cancel the Coriolis and centrifugal terms, so the arm tracks its target even when whipping through the air rather than crawling.
A fast-spinning robot arm extends its outer link and feels it pulled outward all on its own — no motor commanded that pull. A controller that fails to anticipate this centrifugal fling will let the link drift past its target, then correct with a visible jerk.
At high speed a robot's own motion generates forces; a good controller predicts and cancels them so the arm stays on target.
Centrifugal terms come from a single joint's own speed; Coriolis terms come from two joints moving at once. Both depend on velocity, so they disappear whenever the robot is standing still.