Classification of robot manipulators, kinematic modeling, forward and inverse kinematics, velocity kinematics, path planning, point-to-point trajectory planning, dynamic modeling, Euler-Langrange equations, inverse dynamics, joint control, computed torque control, passivity-based control, feedback linearization.
To model, to perform motion planning, and to control a robotic manipulator.
Prof. M.E. Broucke | GB434A | LEC 01 | broucke at control.utoronto.ca |
TBA | GB348 | TUT 01, TUT 02 | TBA at mail.utoronto.ca |
TBA | GB348 | PRA 01, PRA 02 | TBA at mail.utoronto.ca |
TBA | GB348 | PRA 03, PRA 04 | TBA at mail.utoronto.ca |
TBA | GB348 | PRA 05, PRA 06 | TBA at mail.utoronto.ca |
TBA | GB348 | PRA 07, PRA 08 | TBA at mail.utoronto.ca |
Section | TA | Tutorial Dates |
TUT 01, TUT 02 | TBA | Sept 14, Sept 21, Sept 28, Oct 5, Oct 12, Oct 19, Oct 26, Nov 2, Nov 16, Nov 23, Nov 30 |
The following table shows the lecture topics. Note that the lecture schedule may be updated as the semester progresses, so it's a good idea to check the webpage periodically.
Week | Date | Lecture | Topics | Due Dates |
1 | Sept 7 | 1 | Introduction | |
2 | Common kinematic configurations | |||
3 | Rigid motions; Points and vectors; Rotations | |||
2 | Sept 14 | 4 | Rotation matrices; Elementary rotations; Rotational transformations | Tutorial 1 |
5 | Change of reference frame; Composition of rotations | |||
6 | Euler angles; Rigid motions | |||
3 | Sept 21 | 7 | Change of coordinates; Composition of rigid motions; Homogeneous transformations | Tutorial 2 |
8 | Elementary homogeneous transformations; Forward kinematics; DH convention | |||
9 | DH convention exceptions; Examples | |||
4 | Sept 28 | 10 | DH table to homogeneous transformation matrices; Inverse kinematics problem | Tutorial 3 |
11 | Inverse kinematics problem | |||
12 | Inverse orientation problem; Velocity kinematics | Homework 1 | ||
5 | Oct 5 | 13 | Angular velocity | Tutorial 4 |
14 | Instantaneous axis of rotation; Linear velocity; Addition of angular velocities | |||
15 | Robot Jacobian | Lab 1 | ||
6 | Oct 12 | 16 | Inverse velocity kinematics | Tutorial 5 |
17 | Inverse velocity kinematics; End effector forces and torques | |||
18 | Kinematic singularities | Homework 2 | ||
7 | Oct 19 | 19 | Motion planning; Artificial potential approach | Tutorial 6 |
20 | Attractive potential design; Repulsive potential | |||
21 | Repulsive potential; Gradient descent | Lab 2 | ||
8 | Oct 26 | 22 | Spline interpolation | Tutorial 7 |
23 | Decentralized control of robots | |||
24 | Robot modeling: mass particle example | Homework 3 | ||
9 | Nov 2 | 25 | Robot modeling; holonomic constraints; Generalized coordinates | Tutorial 8 |
26 | Virtual displacements; Lagrange D'Alembert principle; Euler-Lagrange equations | |||
27 | Euler Lagrange equation; Kinetic energy of a rigid body | Midterm | ||
Nov 9 | Reading Week | |||
10 | Nov 16 | 28 | Kinetic energy of a rigid body | Tutorial 9 |
29 | Derivation of robot Lagrangian | |||
30 | Equations of motion of a robot; Pendulum on a cart example | Lab 3 | ||
11 | Nov 23 | 31 | Pendulum on a cart example; Double pendulum | Tutorial 10 |
32 | Double pendulum; Centralized Robot control; Feedback linearization | |||
33 | Feedback linearization; Equilibria and stability; Lyapunov's stability theorem | Homework 4 | ||
12 | Nov 30 | 34 | LaSalle's invariance principle | Tutorial 11 |
35 | PD control with gravity compensation | |||
36 | Passivity-based controllers; Adaptive control | Lab 4 |
Homework problems are submitted on Quercus by 5pm on the due date. Homeworks are graded based on (seriously) attempted problems, not correctness. Homeworks that are clearly written and complete are given a mark of 1. Poorly written or incomplete homeworks are given a mark of 0.
Homework | Chapter | Problems | Due Date |
1 | Chapter 2 | 1, 2, 10, 11, 12, 13, 15, 23, 37, 38, 39, 41 | Oct 2 |
2 | Chapter 3 | 2, 3, 4, 5, 6, 7, 13 | Oct 16 |
3 | Chapter 3 | 15, 18; Chapter 4: 13 (swap phi and psi in problem statement), 15, 18, 20 | Oct 30 |
4 | Chapter 7 | 7, 8 (use Euler-Lagrange Method), 12, 13 | Nov 27 |
Labs are Matlab-based and performed in groups of one or two. You may select your own lab partner, or your assigned practical TA will help you form a group. Each group submits a preparation and lab report. Lab preps and reports are submitted on Quercus by 5pm on the due date.
Section | Lab 1 | Lab 2 | Lab 3 | Lab 4 |
PRA 01-08 | Oct 9 | Oct 23 | Nov 20 | Dec 4 |
Labs | 40% | Includes preparation, lab work, and report |
Homework | 10% | |
Midterm | 25% | Friday, November 6 |
Final Exam | 25% | TBA |