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Robotics operators

6 operators in the robotics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
FORWARD_KINEMATICSForward kinematics computing end-effector pose by chaining homogeneous transformation matrices along the kinematic chain of a serial manipulator.T_n^0 = \prod_{i=1}^n A_i(\theta_i)
INVERSE_KINEMATICSResolved-rate inverse kinematics mapping desired end-effector velocity to joint velocities through the inverse of the manipulator Jacobian.\dot{\theta} = J^{-1}(\theta) \dot{x}
JACOBIANManipulator Jacobian matrix relating joint-space velocities to task-space velocities through partial derivatives of the forward kinematic map.J = \frac{\partial x}{\partial \theta}
PATH_PLANNINGA-star search algorithm finding the shortest path by combining actual cost from start with a heuristic estimate of remaining cost to goal.f(n) = g(n) + h(n)
TORQUE_DYNAMICSManipulator equation of motion relating joint torques to inertia, Coriolis and centrifugal effects, and gravitational loading in joint space.\tau = M(\theta)\ddot{\theta} + C(\theta,\dot{\theta})\dot{\theta} + G(\theta)
TRAJECTORY_PLANNINGCubic polynomial trajectory interpolation generating smooth joint-space motion profiles satisfying position and velocity boundary conditions.\theta(t) = a_0 + a_1 t + a_2 t^2 + a_3 t^3

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["FORWARD_KINEMATICS"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​