Robot Modeling and Simulation syllabus

Mathematical Modeling of Robots: Symbolic representation of manipulators, Configuration space, State space, Workspace, Classification of robots (serial, parallel, hybrid), Accuracy and repeatability, Resolution, Wrist and end effectors, Common kinematic arrangements (articulated, SCARA, delta), underactuated and mobile robots. Kinematics of Rigid Bodies: Pose of a rigid body in 3D, Rotation matrices and composition, Euler angles and gimbal lock, Angle-axis representation, Homogeneous transformations, Direct kinematics for typical manipulators, Joint space vs. operational space, Kinematic calibration.

Differential Kinematics and Statics: Geometric Jacobian matrix, Jacobian for typical manipulators, Kinematic singularities, Redundancy analysis, Inverse differential kinematics, Analytical Jacobian, Inverse kinematics algorithms, Statics (force/torque mapping). Trajectory Planning, Actuators & Sensors: Path vs. trajectory, Operational space and joint space trajectories, Joint actuating systems (electric, hydraulic, pneumatic), Proprioceptive sensors (encoders, tachometers), Exteroceptive sensors (force, tactile, proximity).

Dynamics of Robot Manipulators: Lagrange formulation, Properties of dynamic models, Dynamic model of simple manipulators, Parameter identification, Direct and inverse dynamics, Dynamic scaling of trajectories, Operational space dynamic model, Dynamic manipulability ellipsoid. Control Architecture: Functional architecture (task planning, control loops), Programming environment (simulation vs. real-time), Hardware architecture (microcontrollers, DSPs, industrial PCs).

Motion Control: Control problem (tracking desired trajectories), Joint space control, Independent joint PID control, Decentralized control with gravity compensation, Computed torque feedforward control, Centralized control using full dynamics, Operational space control. Force Control: Need for force control in assembly and contact tasks, Compliance control (passive vs. active), Impedance control (regulating inertia, damping, and stiffness), Force control with direct feedback, Constrained motion with natural and artificial constraints, Hybrid force/motion control.

Introduction to Visual Servoing: PD control with gravity compensation, Full inverse dynamics (feedback linearization) control, Nonlinear decoupled feedback control, Resolved motion control in operational space, Adaptive control for robots with unknown or varying parameters. Mobile Robots and Motion Planning: Nonholonomic constraints (no lateral motion), Kinematic models of wheeled robots (differential drive, car-like), Dynamic models, Motion control for trajectory tracking, Odometric localization, Configuration space representation, Planning via retraction, Cell decomposition, Probabilistic planning (RRT, PRM), Planning via artificial potentials.