Math & Kinematics

Singularity

A singularity is a robot configuration at which the manipulator Jacobian loses rank, so the end-effector instantaneously loses the ability to move or exert force in one or more directions. Near singularities, small Cartesian velocities demand unbounded joint velocities, causing erratic high-speed joint motion. Six-axis arms exhibit characteristic wrist, shoulder, and elbow singularities, such as the wrist singularity when joints four and six align.

Why it matters for physical AI

Policies and planners that command Cartesian motion must respect singular regions, since crossing one can trigger joint-speed faults or violent arm motion on real hardware.