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 |
Tian Xia | GB348 | TUT 01, TUT 02 | t.xia at mail.utoronto.ca |
Andrew Lim | GB348 | PRA 01, PRA 02, PRA 03 | andrewwilliam.lim at mail.utoronto.ca |
Mohammad Salehizadeh | GB348 | PRA 07, PRA 08 | m.salehizadeh at mail.utoronto.ca |
Emily Vukovich | GB348 | PRA 04, PRA 05, PRA 06 | emily.vukovich at mail.utoronto.ca |
Section | Day and Time | Location | Dates |
LEC 01 | Mon 11-12 | MC254 | |
Wed 11-12 | MC254 | ||
Thu 11-12 | MC254 | Starts September 6 |
Section | TA | Day and Time | Location | Tutorial Dates |
TUT 01 | Tian Xia | Fri 4-6pm | GB404 | Sept 21, Oct 5, Oct 19, Nov 2, Nov 16, Nov 30 |
TUT 02 | Tian Xia | Mon 9-11am | GB404 | Sept 17, Oct 1, Oct 15, Oct 29, Nov 12, Nov 26 |
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 |
1 | Sept 6 | 1 | Introduction |
2 | Sept 10 | 2 | Common kinematic configurations |
3 | Rigid motions; Points and vectors; Rotations | ||
4 | Rotation matrices; Elementary rotations; Rotational transformations | ||
3 | Sept 17 | 5 | Change of reference frame; Composition of rotations |
6 | Euler angles; Rigid motions | ||
7 | Change of coordinates; Composition of rigid motions; Homogeneous transformations | ||
4 | Sept 24 | 8 | Elementary homogeneous transformations; Forward kinematics; DH convention |
9 | DH convention exceptions; Examples | ||
10 | DH table to homogeneous transformation matrices; Inverse kinematics problem | ||
5 | Oct 1 | 11 | Inverse kinematics problem |
12 | Inverse orientation problem; Velocity kinematics | ||
13 | Angular velocity | ||
6 | Oct 8 | Thanksgiving | |
14 | Instantaneous axis of rotation; Linear velocity; Addition of angular velocities | ||
15 | Robot Jacobian | ||
7 | Oct 15 | 16 | Inverse velocity kinematics |
17 | Inverse velocity kinematics; End effector forces and torques | ||
18 | Kinematic singularities | ||
8 | Oct 22 | 19 | Motion planning; Artificial potential approach |
20 | Attractive potential design; Repulsive potential | ||
21 | Repulsive potential; Gradient descent | ||
9 | Oct 29 | 22 | Spline interpolation |
23 | Decentralized control of robots | ||
24 | Robot modeling: mass particle example | ||
10 | Nov 5 | 25 | Robot modeling; holonomic constraints; Generalized coordinates |
26 | Virtual displacements; Lagrange D'Alembert principle; Euler-Lagrange equations | ||
27 | Euler Lagrange equation; Kinetic energy of a rigid body | ||
11 | Nov 12 | 28 | Kinetic energy of a rigid body |
29 | Derivation of robot Lagrangian | ||
30 | Equations of motion of a robot; Pendulum on a cart example | ||
12 | Nov 19 | 31 | Pendulum on a cart example; Double pendulum |
32 | Double pendulum; Centralized Robot control; Feedback linearization | ||
33 | Feedback linearization; Equilibria and stability; Lyapunov's stability theorem | ||
13 | Nov 26 | 34 | LaSalle's invariance principle |
35 | PD control with gravity compensation | ||
36 | Passivity; passivity-based control | ||
14 | Dec 3 | 37 | Passivity-based controllers; Adaptive control |
38 | Adaptive passivity-based control and computer demo |
Homework problems are turned in at the beginning of the lecture on the dates below. 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 10 |
2 | Chapter 3 | 2, 3, 4, 5, 6, 7, 13 | Oct 22 |
3 | Chapter 3 | 15, 18; Chapter 4: 13 (swap phi and psi in problem statement), 15, 18, 20 | Nov 19 |
4 | Chapter 7 | 7, 8 (use Euler-Lagrange Method), 12, 13 | Dec 3 |
Labs take place in BA3114 and are performed in groups of two or three students. Lab groups are formed in the first lab. There are no make-up labs. You may not switch lab sections. Lab 0 is an introduction to the KUKA robots and has no preparation or report. For Labs 1-4, each group submits a preparation at the beginning of the lab. One week after the lab, each lab group submits a lab report.
Section | Day and Time | Lab 0 | Lab 1 | Lab 2 | Lab 3 | Lab 4 |
PRA 01 | Fri 9-12 | Sept 21 | Oct 19 | Nov 2 | Nov 16 | Nov 30 |
PRA 02 | Fri 9-12 | Sept 14 | Oct 12 | Oct 26 | Nov 9 | Nov 23 |
PRA 03 | Mon 15-18 | Sept 24 | Oct 22 | Nov 5 | Nov 19 | Dec 3 |
PRA 04 | Mon 15-18 | Sept 17 | Oct 15 | Oct 29 | Nov 12 | Nov 26 |
PRA 05 | Wed 15-18 | Sept 26 | Oct 24 | Nov 7 | Nov 21 | Dec 5 |
PRA 06 | Wed 15-18 | Sept 19 | Oct 17 | Oct 31 | Nov 14 | Nov 28 |
PRA 07 | Thu 15-18 | Sept 20 | Oct 18 | Nov 1 | Nov 15 | Nov 29 |
PRA 08 | Thu 12-15 | Sept 20 | Oct 18 | Nov 1 | Nov 15 | Nov 29 |
Labs | 20% | Includes preparation, lab work, and report |
Homework | 5% | |
Midterm | 25% | Monday, October 29, 6-8pm |
Final Exam | 50% | TBA |