Syllabus Introduction To Ro

Syllabus Introduction To Ro

botics

Introduction

- Introduction to robotics: What is a robot? Robots History. Robot classification. Evolution toward Industrial robots. Other kind of robots: service robots, exoskeletons. Under-actuated robots: underwater robots, space robots, drones, legged robots, humanoids, quadrupeds.

- Robot’s functional units: Mechanical Structure: joints, links, end-effector, workspace, robot classification based on joint arrangement. Overview of functional units of a robot: sensors, actuators, etc. Overview of the main robotics topics: control, perception, estimation, planning.

Sensors

- Introduction to measurement: properties of a measurement system (accuracy, repeatability, uncertainty), sensors characteristics (sensitivity, range, resolution, dynamic response), type of measurements errors (systematic, random). Non idealities in sensors: non-linearity, offset, scaling, dead-band, hysteresis.

- Proprioceptive sensors: Types of (propio-ceptive) sensors. Position sensors (potentiometers, relative/absolute encoders) quantization noise, contact switches, LDR, inertial sensors (accelerometers, gyros).

- Exteroceptive sensors: Types of extero-ceptive sensors. Force sensors (strain gauges, reading/mounting of strain gauges, wheatstone bridge, F/T 6 axis force sensors). Vision sensors. Passive cameras, stereo camera, triangulation in stereo-vision. Camera modeling (pinhole model), camera calibration. Active sensors: LiDAR, Structured light sensors, basic image processing, visual odometry, state estimation, point cloud. Proxy-sensors.

- Signal processing: Analog/discrete signals. Sampling, quantization and reconstruction (A/D, D/A converters). Problems in digital implementation: quantization errors, delays, aliasing (Nyquist theorem). Low-pass filter (discrete implementation). Basic signal processing: average, moving average, weighted average.

Actuators

- Typer of actuators: types of actuators in robotics: pneumatic, hydraulic actuators, EHAs, electric motors, Series elastic actuators.

- Electrical actuators: Review of some useful notions of physics. Synchronous/ Asynchronous AC Motor, brushed/brushless DC Motor, efficiency, model of a DC motor steady state response. Motor control : voltage / current.

- Transmissions: types of transmissions, modeling transmission, gearbox, Optimal choice of reduction ratio, modeling elasticity in transmission.

- Non idealities: Non idealities in actuators: modeling friction, back-lash, dead-band

- Simulation of actuators: Simulation of actuators: state space dynamics of a DC motor, discrete equivalent model, integration of dynamics, time responses.

Control basics

- Introduction to control: open loop control, feed-back concept, bang-bang controller, transient/steady-state response, static/dynamic control specifications, design of a controller.

- PID: P, PD, PID control, current control, anti-windup technique

- Implementation of PID: realizability issue of PID, Digital PID, tuning techniques for PID.

Kinematics:

- Kinematics of a rigid body Position and orientation of a rigid body. Reference frames. Rotation matrices (properties, composition, and interpretations). Derivative of a rotation matrix. Minimal representations of orientation. Skew-symmetric matrices. Exponential maps and the Rodríguez formula. Euler angles. Relation between Euler rates and angular velocity. Unit quaternions.

- Manipulator direct kinematics: Definition of forward and inverse kinematics. Joint, task and actuation spaces. Generalized coordinates. Forward kinematics of robot manipulators. Homogeneous transformations (properties, composition and interpretations). Inverse of a homogeneous transformation matrix. Frame placement. Direct kinematics of a kinematic chain.

- Inverse Kinematics: Definition of inverse kinematics. Solvability and workspace. Closed form (analytical) solutions. Examples.

- Direct Differential Kinematics: Linear and angular velocity of a rigid body. Linear and velocity of a manipulator link driven from prismatic or revolute joints. Contribution of prismatic and revolute joints to end-effector velocity. The Geometric Jacobian. The Analytical Jacobian. Relationship between Geometric and Analytical Jacobian.

- Numerical Inverse Kinematics: Gauss-Newton iterative approach. Pathological cases . Line search. Discussion on multiple solutions.

- Redundancy and Singularities: Definition of redundancy. Redundant manipulators. Primer on linear algebra sub-spaces. Redundancy and vector null space. The pseudo-inverse. Geometric interpretation of inverse kinematics mapping. Singular values. Definition of singularity. Types of singularities. Inverse differential kinematics and singularities. Damped least-squares method. Higher order differential inversion.

Dynamics:

- Statics: statics vs. dynamics. Principle of virtual works. Kineto-static duality and analysis of sub-spaces. Velocity and force transformations.

- Dynamic of a rigid body: Kinetic energy of a rigid body. Examples of moments of inertia. Potential gravitational energy. Euler-Lagrange method. Contribution of non consevative forces. Linearity of the model in the dynamic parameters. Analysis of inertial couplings, Coriolis and centrifugal effects. Recursive Newton-Euler method. Examples.

- Interaction dynamics: Rigid and compliant contact models. Constrained robot dynamics. Simulation with a compliant contact model.

- Under-actuation: Definition and examples of under-actuated robots. Modeling of floating base robots. Structure of the floating base dynamics.

Joint Space control

- PID for manipulators: Overview of control problems in robotics. The concept of stability. PD, PD + gravity compensation, PID control.

- Inverse dynamics. Decentralized vs. centralized control. Feedback linearization in robotics. Joint space Inverse dynamics (Computed torque).

Task Space Control

- Cartesian space control: inverse kinematics control, direct Cartesian space control. Cartesian PD, PD+ gravity compensation. Inverse dynamics in Cartesian space (non-redundant and redundant case).

- Orientation Control: orientation control with different parametrization of orientation (rotation matrix, angle-axis, Euler angle, quaternions).

- Interaction Control: Applications. passive/ active methods. Direct force control. Cartesian space impedance control, concept of inertia shaping. Superimposition of impedances. Simplified formulations. Compliance control. Selection of impedance parameters. Torsional impedance. Admittance control. Visual servoing.

Lab sessions

- Lab Python: introductory lecture to python programming and to the usage of the numpy library

- Lab Control: simulation and control of a DC motor, PID design and tuning (Matlab).

- Lab Kinematics/Dynamics: learn to build a robot model using the Unified Robot Description Format (URDF), compute the direct/inverse kinematics of a 4-DoF serial manipulator. Design a reference trajectory with polynomials. Implement the numerical inverse kinematics. Compute and analyze the forward/inverse dynamics of a 4-DoF serial manipulator using the Recursive Newton-Euler Algorithm (RNEA).

- Lab Joint Space Control: design motion controllers (of increasing complexity) in the joint space for a manipulator in free-motion. Implement a centralized approach (i.e. inverse dynamics). Implement the interaction with the environment with a compliant contact model.

- Lab Task Space Control: design a motion controllers (of increasing complexity) in the task space for a manipulator in free-motion. Implement a centralized approach (i.e. inverse dynamics). Implement the control of the orientation using the angle-axis representation.