Robot control
Jerk
Definition
Jerk is the rate at which acceleration changes with time, or the third time derivative of position. Robotics uses jerk limits to constrain how abruptly a commanded motion changes acceleration.
Updated
How quickly acceleration changes
A joint can have modest acceleration yet change that acceleration abruptly. Jerk describes this change. For a linear coordinate, its units are metres per second cubed; for a joint angle, radians per second cubed.
Modern Robotics contrasts a trapezoidal velocity profile, whose acceleration jumps between phases, with an S-curve profile that changes acceleration through finite-jerk segments.
Velocity, acceleration, and jerk need separate limits
Limiting acceleration does not bound the rate at which acceleration changes. Conversely, zero jerk can accompany a large constant acceleration. These are different constraints on a trajectory.
The Ruckig motion generator accepts separate velocity, acceleration, and jerk constraints when calculating motion between states defined by position, velocity, and acceleration. This makes jerk a practical parameter in trajectory generation, including motions commanded through joint-space control.
A jerk limit does not specify every aspect of motion
A piecewise-constant jerk profile can keep acceleration continuous while jerk itself changes at segment boundaries. “Jerk-limited” therefore does not necessarily mean jerk-continuous.
The chosen coordinate also matters: a bound on a joint's angular jerk is not automatically the same as a bound on Cartesian hand jerk. Robot geometry and the full motion determine that relationship.
Sources
Related terms
Trajectory optimization
Trajectory optimization finds a time-varying motion, and often control inputs, that minimizes an objective while satisfying specified constraints. Robot applications can include geometric, kinematic, and dynamic constraints.
Joint-space control
Joint-space control expresses a robot's motion targets and tracking errors in joint coordinates, such as joint angles or linear displacements. It regulates those coordinates rather than defining the primary motion error directly at the end-effector.
Motion planning
Motion planning finds a robot movement from an initial state to a goal while satisfying constraints such as collision avoidance. A planner may produce a geometric path, a timed trajectory, or a sequence of controls.