Mechatronics & Automation

Robotics integrates MEC (mechanical engineering), EE (electrical engineering), and CS (computer science) into systems that sense, decide, and act in the physical world. This pack covers the core subsystems, control theory, and practical design patterns for robotic systems.

Robot Kinematics

KIN (kinematics) describes robot motion without considering forces. A robot manipulator is a kinematic chain of rigid links connected by joints. Revolute joints (R) provide rotational DOF (degrees of freedom); prismatic joints (P) provide linear DOF. A 6-DOF manipulator can reach any position and orientation in its WS (workspace) — the reachable volume.

FK (forward kinematics) computes end-effector position and orientation given joint angles. DH (Denavit-Hartenberg) convention assigns coordinate frames to each link using four parameters: link length (a), link twist (alpha), link offset (d), joint angle (theta). The homogeneous transformation matrix for each joint multiplies sequentially: T_0n = T_01 * T_12 * ... * T_(n-1)n.

IK (inverse kinematics) solves the reverse problem: given desired end-effector pose, find joint angles. IK is generally harder than FK — may have multiple solutions, no solution (outside WS), or singularities. Analytical IK (closed-form) is preferred when possible (6R with spherical wrist). Numerical IK uses iterative methods: Jacobian transpose, Jacobian pseudo-inverse, or damped least squares (DLS) to handle singularity-adjacent configurations.

The Jacobian matrix J maps joint velocities to end-effector velocities: v = J * dq/dt. At singularities, J loses rank — the manipulator cannot move in certain Cartesian directions regardless of joint velocities. Singularity avoidance or singularity-robust control is essential for smooth operation.

Dynamics & Control

DYN (dynamics) describes forces and torques causing motion. The equation of motion: tau = M(q)*qdd + C(q,qd)*qd + g(q), where M is the inertia matrix, C captures Coriolis and centrifugal effects, g is gravity, tau is joint torques. Computed torque control uses the full DYN model to linearize and decouple joint control.

PID control is the workhorse of robot joint control. Proportional (P) drives error toward zero, Integral (I) eliminates steady-state error, Derivative (D) provides damping. Tuning: start with P only, increase until oscillation, add D to stabilize, add I to eliminate offset. Cascade control with inner velocity loop and outer position loop improves disturbance rejection.

IMPC (impedance control) regulates the dynamic relationship between force and motion rather than tracking a rigid trajectory. The robot behaves as a virtual spring-damper system: F = Kp*(xd - x) + Kd*(vd - v). This enables compliant behavior essential for contact tasks — assembly, polishing, human-robot interaction. Admittance control (force input, motion output) is the dual formulation for stiff actuators.

Trajectory planning generates smooth paths in joint space or Cartesian space. Trapezoidal velocity profiles (acceleration, cruise, deceleration) are simple but have discontinuous acceleration. Cubic and quintic polynomials provide smoother profiles. In Cartesian space, linear interpolation with spherical linear interpolation (SLERP) for orientation ensures predictable tool paths.

Actuators & Drive Systems

DC motors dominate small-to-medium robots. Brushed DC: simple control (PWM voltage modulation), moderate efficiency. BLDC (brushless DC): higher efficiency, longer life, requires electronic commutation (ESC — electronic speed controller). Motor selection: torque = kt * I (torque constant times current), speed = V/ke (voltage over back-EMF constant).

Gearing reduces motor speed and amplifies torque by gear ratio N. Harmonic drives (strain wave gearing) provide high ratios (50-160:1) in compact packages with zero backlash — standard in collaborative robot joints. Cycloidal drives offer similar benefits with higher shock resistance. Backlash in conventional gear trains introduces positioning error and limit cycle oscillations in control.

SEA (series elastic actuator) places a compliant element between motor and load. The spring provides: force sensing (measure spring deflection), energy storage (jumping, impact absorption), inherent compliance for safe human interaction. VSA (variable stiffness actuator) can adjust compliance dynamically — stiff for precision, compliant for safety.

Linear actuators: ball screws (high precision, efficiency ~90%), lead screws (self-locking, lower efficiency), belt drives (high speed, lower precision), pneumatic cylinders (compliant, high force-to-weight, difficult to control precisely).

Sensing & Perception

ProprioCEP (proprioceptive) sensors measure internal state: encoders (incremental and absolute) for joint position, tachometers for velocity, current sensors for torque estimation, IMU (inertial measurement unit — accelerometer + gyroscope) for body orientation.

ExteroCEP (exteroceptive) sensors perceive the environment: LIDAR (laser ranging, 360-degree 2D or 3D point clouds), depth cameras (structured light — Intel RealSense, or ToF — time of flight), stereo cameras (depth from disparity), force/torque sensors (6-axis, strain gauge based) at wrist for contact detection.

Computer vision for robotics: object detection (YOLO, SSD — real-time bounding boxes), pose estimation (6DOF object pose from RGB or depth), visual SLAM (simultaneous localization and mapping — ORB-SLAM, LSD-SLAM). Point cloud processing with PCL (Point Cloud Library): plane segmentation, clustering, registration (ICP — iterative closest point).

Mobile Robotics

LOC (localization) determines the robot's position in a known map. Probabilistic approaches: particle filter (Monte Carlo localization) maintains a set of position hypotheses weighted by sensor likelihood. EKF (Extended Kalman Filter) fuses odometry with external measurements (GPS, LIDAR scan matching, visual features) for state estimation.

SLAM solves the chicken-and-egg problem: building a map while simultaneously localizing within it. Graph-based SLAM represents poses as nodes and constraints as edges — optimization (g2o, GTSAM) minimizes constraint errors. Loop closure detection (recognizing previously visited locations) corrects accumulated drift.

PATH planning: global planners (A*, RRT — Rapidly-exploring Random Trees, PRM — Probabilistic Roadmaps) find paths in configuration space. Local planners (DWA — Dynamic Window Approach, TEB — Timed Elastic Bands) generate real-time velocity commands avoiding dynamic obstacles. The costmap (2D or 3D occupancy grid) represents traversability — inflated obstacles account for robot footprint.

ROS (Robot Operating System) provides middleware infrastructure: publish-subscribe messaging (topics), request-response services, parameter server, and TF (transform) tree for coordinate frame management. ROS 2 uses DDS (Data Distribution Service) for real-time communication with QoS policies. Navigation stack (nav2 in ROS 2) integrates localization, costmaps, and planning into a complete autonomous navigation solution.

Manipulation & Grasping

Grasp planning: force closure (contact forces can resist any external wrench) vs form closure (geometry constrains all motion). Antipodal grasps (parallel-jaw gripper) work for many objects. Grasp quality metrics include wrench space volume and minimum singular value of the grasp matrix.

Grasp synthesis from perception: analytical methods require object models; data-driven approaches (GraspNet, Contact-GraspNet) predict grasp poses directly from point clouds. Suction grippers complement parallel-jaw for flat surfaces. Soft grippers (pneumatic, jamming) adapt to irregular shapes.

Pick-and-place pipeline: perceive (segment object from scene), plan grasp (approach vector, pre-grasp pose), plan motion (collision-free trajectory to grasp pose), execute (approach, close gripper, verify grasp, retract, place). MoveIt (ROS manipulation framework) provides motion planning with OMPL (Open Motion Planning Library) backend, collision checking, and IK integration.