Hardware & control
Robot kinematics
Robot kinematics describes the geometric relationship between a robot’s joint configuration and the position, orientation and velocity of its links or end-effector, without modelling the forces that cause the motion. Forward kinematics computes pose from joint values; inverse kinematics searches for joint values that achieve a requested pose.
Also known as: kinematics, robotic kinematics
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Forward and inverse kinematics
Forward kinematics evaluates a geometric model of the robot. Given joint angles or displacements, it returns the pose of an end-effector or another link in a declared reference frame.
Inverse kinematics asks the opposite question: which joint configuration produces a requested pose? A target may have no solution, one solution or several solutions. Numerical solvers therefore minimise pose error while enforcing joint limits, collision constraints and other feasibility checks.
The Jacobian and differential motion
Velocity kinematics uses a configuration-dependent Jacobian matrix to relate joint velocity to end-effector velocity. Modern Robotics Chapter 5 also shows how loss of Jacobian rank identifies kinematic singularities, where motion in one or more task-space directions becomes unavailable.
Differential inverse kinematics uses that local relationship to calculate joint velocities for a desired end-effector velocity. A pseudoinverse gives a least-squares solution, but practical controllers often add damping, joint-limit handling and collision constraints.
Why kinematic metadata matters
Kinematic quantities are meaningful only with the robot model and coordinate frames that generated them. A dataset should state joint order, angle or distance units, base frame, end-effector frame, calibration and whether a pose was measured, estimated or computed from forward kinematics.
Kinematics alone does not predict inertia, force, friction, compliance or contact response. Those belong to dynamics and control, even though a deployed controller commonly uses both kinematic and dynamic information.
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Related terms
Hardware & control
Degree of freedom
A degree of freedom (DoF) is one independent parameter needed to specify a robot’s configuration; equivalently, a robot’s DoF is the dimension of its configuration space. It describes possible motion, not the number of motors. Joint constraints, closed kinematic chains and environmental contacts can make joint count, actuator count and controllable motion differ.
Hardware & control
End effector
An end effector is a task-specific device attached to a robot manipulator’s mechanical interface so the robot can act on its environment, such as a gripper, hand or welding tool. It is distinct from the wrist or mounting flange, and from the tool centre point, which is only a coordinate frame used to plan the device’s motion.
Data & collection
Trajectory
A trajectory is a time-ordered sequence of states or observations, actions and, where applicable, rewards generated as an agent or robot evolves. A complete episode or policy rollout often yields a trajectory, but the terms are not universally identical: trajectories may be partial, while episodes have dataset- or environment-defined boundaries.
Hardware & control
Actuator
An actuator is a robot’s power mechanism that converts electrical, hydraulic, pneumatic or other supplied energy into controlled mechanical force, torque or motion. In a humanoid, actuators drive joints, often through transmissions; they are distinct from the joints and sensors, and their arrangement need not correspond one-to-one with the robot’s degrees of freedom.