The Robotics Manual
Glossary

Glossary

A comprehensive reference of essential robotics, kinematics, control, and Physical AI terms

Overview

Welcome to the Robotics Manual Glossary. Whether you are building your first robot arm, designing a closed-loop controller, or training a vision-language-action model, robotics combines terminology from mechanical engineering, electrical hardware, control theory, and machine learning.

Use this reference to quickly look up core terms, coordinate systems, hardware primitives, and Physical AI concepts.

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Core Concepts & Embodiment

Embodied AI (Physical AI)

Artificial intelligence systems situated in physical bodies that perceive the real world through sensors and interact with it through physical actuators. Unlike digital-only models, embodied systems must operate under the constraints of physics, uncertainty, latency, and real-time feedback.

Sense-Think-Act Loop

The continuous cycle governing robotic operation:

  1. Sense: Capture observations through proprioceptive and exteroceptive sensors.
  2. Think: Process sensory signals, estimate state, and compute control decisions or model predictions.
  3. Act: Issue motor commands to physical actuators to influence the physical environment.

Degrees of Freedom (DoF)

The number of independent variables or axes required to uniquely define the position and orientation of a mechanical system in space. A free rigid body in 3D space possesses 6 DoF: 3 translational (X, Y, Z) and 3 rotational (Roll, Pitch, Yaw).

End-Effector

The device or tool mounted at the distal end of a robotic manipulator designed to interact directly with the environment or manipulate objects. Common examples include parallel-jaw grippers, suction cups, multi-fingered dexterous hands, and specialized welding or machining tools.

Workspace (Work Envelope)

The total continuous 3D volume that the robot's end-effector can physically reach. The workspace is determined by the kinematic architecture, link lengths, and joint limits of the robot.

Payload Capacity

The maximum external weight that a robot manipulator can safely carry, position, and accelerate while maintaining nominal speed, repeatability, and control stability.

Repeatability

The ability of a robot to return to the exact same position and orientation when commanded to repeat the same trajectory under identical operating conditions. In modern manipulators, repeatability is often on the order of sub-millimeters.

Accuracy

The degree of closeness between a commanded target coordinate in space and the actual coordinate reached by the robot end-effector. Repeatability measures consistency; accuracy measures absolute positioning truth.

Rigid Body

An idealized physical body in which deformations under applied loads are negligible, meaning the Euclidean distance between any two given points remains invariant during motion.

Kinematics, Dynamics & Geometry

Kinematics

The branch of mechanics describing the geometry of motion—positions, velocities, and accelerations—without considering the forces, torques, or masses that produce that motion.

Forward Kinematics (FK)

The mathematical process of calculating the Cartesian pose (position and orientation) of the end-effector given the known joint angles and link geometry of the robot: x = f(q)

Inverse Kinematics (IK)

The mathematical process of calculating the joint angles required to achieve a desired Cartesian pose of the end-effector: q = f⁻¹(x) IK may have zero solutions (if the target is out of reach), a unique solution, or multiple valid configurations (e.g., elbow-up vs. elbow-down).

Jacobian Matrix (J)

A matrix of partial derivatives that maps joint velocities to Cartesian velocities of the end-effector: ẋ = J(q) · q̇ The Jacobian transpose is also used to map Cartesian forces and moments at the end-effector to equivalent joint torques: τ = Jᵀ · F.

Kinematic Singularity

A specific joint configuration where the Jacobian matrix loses full rank. At a singularity:

  • The robot loses the ability to move in one or more Cartesian directions.
  • Small Cartesian commands can demand mathematically infinite joint velocities.
  • Standard inverse kinematics solvers become numerically unstable.

Cartesian Space (Task Space / Operational Space)

The coordinate space representing the real-world operational environment, typically specified by 3D coordinates (X, Y, Z) and orientation (Euler angles, rotation matrices, or quaternions).

Joint Space (Configuration Space / C-Space)

The coordinate space defined by the values of each of the robot's individual joints (e.g., radians for rotary joints, meters for linear prismatic joints). An n-DoF robot has an n-dimensional configuration space.

Tool Center Point (TCP)

The reference point and coordinate frame located at the working tip of the end-effector. All motion trajectories, waypoint targets, and coordinate transformations are typically calculated relative to the TCP.

Base Frame (World Frame)

The fixed, stationary reference coordinate frame anchored at the foundation of the robot or its environment, serving as the universal reference for all subordinate coordinate transformations.

Quaternions

A four-dimensional number representation (w, x, y, z) used to represent 3D spatial rotations. Unlike Euler angles (Roll, Pitch, Yaw), quaternions avoid gimbal lock and provide smooth, unambiguous spherical linear interpolation (SLERP).

Actuators, Motors & Transmissions

Actuator

A hardware transducer that converts stored energy (typically electrical, pneumatic, or hydraulic) into controlled mechanical motion (rotary or linear).

Brushless DC (BLDC) Motor

An electric motor that uses permanent magnets on the rotor and electronically commutated windings on the stator. BLDC motors provide high torque-to-weight ratios, high efficiency, minimal thermal dissipation, and long operational lifespans.

Stepper Motor

A brushless DC motor whose rotor rotates in discrete, uniform angular increments (steps). Stepper motors can achieve open-loop positional hold without requiring an encoder, but can stall or skip steps under excessive loads.

Servomotor (Servo)

An integrated actuation unit combining an electric motor, a gear reduction mechanism, a position/velocity sensor (such as an encoder or potentiometer), and an embedded closed-loop controller.

Harmonic Drive (Strain Wave Gear)

A precision gearbox mechanism composed of three components: a wave generator, a flexible cup (flexspline), and a rigid circular spline. Harmonic drives deliver exceptionally high reduction ratios (e.g., 50:1 to 160:1) in a compact, lightweight form factor with near-zero backlash.

Cycloidal Drive

A speed reducer utilizing an eccentric cam and cycloidal disc pins. Cycloidal drives distribute contact loads across multiple teeth simultaneously, providing high shock resistance, compact dimensions, and zero or negligible backlash.

Planetary Gearbox

A transmission mechanism consisting of a central sun gear, multiple orbiting planet gears, a planet carrier, and an outer ring gear. It offers balanced load sharing, compact coaxial alignment, and moderate gear reduction ratios.

Backlash

The clearance, play, or lost motion between mating gear teeth when rotational direction is reversed. Backlash introduces positioning errors and unmodeled hysteresis into kinematic chains.

Backdrivability

The ease with which an external force applied at an actuator's output shaft can drive the motor in reverse. High backdrivability allows a robot to safely yield under external contact, sense contact forces passively, and support fluid manual hand guiding during teleoperation.

Quasi-Direct Drive (QDD)

An actuation architecture pairing a high-torque, low-speed motor with a low gear reduction ratio (typically 5:1 to 10:1). QDD actuators feature high backdrivability, high force-transparency, and compliance without requiring expensive torque sensors.

Tendon-Driven Mechanism

A transmission system that uses flexible cables (tendons) routed over pulleys or inside guide sheaths to transmit tensile force from base-mounted actuators to distal joints, drastically minimizing the moving mass of robot limbs.

Sensors, Perception & State Estimation

Proprioception

The sensing of the robot's own internal mechanical and electrical states, such as joint positions, joint angular velocities, motor temperatures, and electrical currents.

Exteroception

The sensing of the external environment outside the robot's physical body, including visual appearance, spatial depth, proximity, ambient sounds, and surface contact forces.

Optical & Magnetic Encoders

Sensors attached to motor shafts or joint pivots that measure rotational position and speed:

  • Incremental encoders: Report relative pulse counts from an arbitrary startup zero point.
  • Absolute encoders: Report exact angular position immediately upon power-up without requiring a homing sequence.

Inertial Measurement Unit (IMU)

A sensor cluster combining multi-axis accelerometers and gyroscopes (and occasionally magnetometers) to measure linear acceleration, angular velocity, and orientation in three dimensions.

RGB-D Camera

An imaging sensor that captures synchronized color video (RGB) along with per-pixel spatial depth (D). Common depth sensing modalities include structured light projection, active infrared stereo, and time-of-flight (ToF).

Point Cloud

A collection of discrete 3D spatial data points [X, Y, Z] (often with color [R, G, B] or intensity) representing the physical surfaces of objects in the robot's environment.

Force-Torque (F/T) Sensor

A multi-axis transducer, frequently mounted at the robot wrist or foot, that measures the three orthogonal forces (Fx, Fy, Fz) and three orthogonal moments (Mx, My, Mz) exerted on the tool or environment.

Tactile Sensor (Tactile Skin)

A contact sensor array distributed over a robot gripper or fingertip that detects pressure distributions, shear stresses, and tactile slip to facilitate gentle grasping and slip detection.

Sensor Fusion

Algorithmic integration of data from multiple disparate sensors (e.g., combining camera vision, joint encoders, and an IMU via an Extended Kalman Filter) to produce a unified, low-noise estimate of state that outperforms any individual sensor stream.

Control Systems & Feedback

Closed-Loop Control (Feedback Control)

A control paradigm where the system continuously observes its actual output state, compares it with a desired reference target to compute an error signal, and commands actuators to drive the error toward zero.

Open-Loop Control

A control architecture where commands are executed purely based on a model or schedule without measuring the resulting real-world outcome or compensating for unexpected external disturbances.

PID Controller

A ubiquitous feedback controller that computes control effort based on three error terms:

  • Proportional (P): Acts proportionally to the current error.
  • Integral (I): Accumulates past error over time to eliminate steady-state drift.
  • Derivative (D): Evaluates the rate of change of error to anticipate future behavior and dampen oscillations.

Impedance Control

A compliant control strategy where the robot's end-effector is programmed to emulate a virtual mass-spring-damper system. Instead of strictly enforcing a rigid Cartesian trajectory, the controller regulates the relationship between external contact forces and resulting displacements.

Admittance Control

The dual of impedance control: the robot measures contact forces using an external force sensor and computes a compliant displacement or velocity trajectory to accommodate the load.

Torque Control

A low-level control mode where joint motors are commanded to exert specific torques (currents) directly, rather than tracking position or velocity setpoints. Torque control is essential for dynamic motions, gravity compensation, and safe physical contact.

Gravity Compensation

A feedforward algorithm that computes the gravitational torques exerted on each link of a manipulator based on its current pose and mass distribution, applying equal counter-torques so the arm feels virtually weightless to external touch.

Control Frequency & Latency

  • Frequency: The rate at which the digital controller executes its sense-compute-command loop (typically 100 Hz to 1,000 Hz or higher for high-performance joint control).
  • Latency: The time lag between a physical event occurring, the sensor registering the measurement, the compute stack selecting an action, and the motor generating mechanical force.

Physical AI, Learning & Teleoperation

Vision-Language-Action (VLA)

Multimodal foundation models trained end-to-end to ingest RGB camera frames and natural language instructions, and directly predict low-level robot control actions (e.g., end-effector Cartesian delta poses or joint targets).

Imitation Learning (Behavioral Cloning)

A machine learning approach where a policy is trained via supervised learning to clone human expert demonstrations, mapping observed states s_t to actions a_t.

Diffusion Policy

A robot policy architecture that models complex, multi-modal action trajectories using a conditional denoising diffusion probabilistic model, capable of learning diverse strategies for contact-rich manipulation.

Teleoperation

The practice of operating a physical robot remotely in real time using an intuitive input device (such as a bilateral leader arm, VR hand tracking, or 6-DoF spacemouse), widely used to collect high-quality demonstration datasets.

Human Intervention

An event during autonomous policy execution where a human operator intervenes to correct an error, recover from failure, or guide the robot past an ambiguous state. In continuous learning systems like Humaan, interventions provide the most informative negative-and-correction training signal.

Robot Experience

The persistent, semantically enriched record of a robot attempting a task in a specific environment. A complete experience captures synchronized sensor observations, policy actions, execution timeline events, failures, interventions, and final outcomes.

Sim-to-Real Transfer

The methodology of training policies within high-throughput physics simulators (e.g., MuJoCo, Isaac Sim) and transferring the learned weights to physical hardware.

Domain Randomization

A sim-to-real technique where visual attributes (lighting, colors, textures) and physical dynamics (masses, friction, actuator delays) are randomized during simulation training, enabling policies to generalize robustly to real-world variations without overfitting.

Policy

A computational model or decision rule π(a_t | o_t) that takes the current sensory observations o_t (images, joint states, history) and outputs the next action a_t for the robot to execute.

Humaan Loop

The continuous improvement lifecycle for embodied intelligence: capturing real-world experiences, curating learning datasets, training and adapting policies, benchmarking against standardized evaluations, and deploying verified models back to physical robots.

PreviousSensors and Actuators