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 |
Ruthrash Hari | GB348 | PRA 01, PRA 02 | ruthrash.hari at mail.utoronto.ca |
Vipin Karthikeyan | GB348 | PRA 03, PRA 04 | vipin.karthikeyan at mail.utoronto.ca |
Andrew Lim | GB348 | PRA 05, PRA 06 | andrewwilliam.lim at mail.utoronto.ca |
Sajad Salmanipour | GB348 | PRA 07, PRA 08 | s.salmanipour at mail.utoronto.ca |
Section | Day and Time | Location | Dates |
LEC 01 | Mon 11-12 | GB119 | |
Wed 11-12 | GB119 | ||
Thu 11-12 | GB119 | Starts September 5 |
Section | TA | Day and Time | Location | Tutorial Dates |
TUT 01 | Tian Xia | Mon 12-14 | BA2184 | Sept 23, Oct 7, Oct 21, Nov 4, Nov 18, Dec 2 |
TUT 02 | Tian Xia | Mon 12-14 | BA2184 | Sept 16, Sept 30, Oct 14, Oct 28, Nov 11, Nov 25 |
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 5 | 1 | Introduction |
2 | Sept 9 | 2 | Common kinematic configurations |
3 | Rigid motions; Points and vectors; Rotations | ||
4 | Rotation matrices; Elementary rotations; Rotational transformations | ||
3 | Sept 16 | 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 23 | 8 | Elementary homogeneous transformations; Forward kinematics; DH convention |
9 | DH convention exceptions; Examples | ||
10 | DH table to homogeneous transformation matrices; Inverse kinematics problem | ||
5 | Sept 30 | 11 | Inverse kinematics problem |
12 | Inverse orientation problem; Velocity kinematics | ||
13 | Angular velocity | ||
6 | Oct 7 | 14 | Instantaneous axis of rotation; Linear velocity; Addition of angular velocities |
15 | Robot Jacobian | ||
16 | Inverse velocity kinematics | ||
7 | Oct 14 | Thanksgiving | |
17 | Inverse velocity kinematics; End effector forces and torques | ||
18 | Kinematic singularities | ||
8 | Oct 21 | 19 | Motion planning; Artificial potential approach |
20 | Attractive potential design; Repulsive potential | ||
21 | Repulsive potential; Gradient descent | ||
9 | Oct 28 | 22 | Spline interpolation |
23 | Decentralized control of robots | ||
24 | Robot modeling: mass particle example | ||
10 | Nov 4 | 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 11 | 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 18 | 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 25 | 34 | LaSalle's invariance principle |
35 | PD control with gravity compensation | ||
36 | Passivity; passivity-based control | ||
14 | Dec 2 | 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 7 |
2 | Chapter 3 | 2, 3, 4, 5, 6, 7, 13 | Oct 21 |
3 | Chapter 3 | 15, 18; Chapter 4: 13 (swap phi and psi in problem statement), 15, 18, 20 | Nov 18 |
4 | Chapter 7 | 7, 8 (use Euler-Lagrange Method), 12, 13 | Dec 2 |
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 | Thu 12-15 | Sept 19 | Oct 17 | Oct 31 | Nov 14 | Nov 28 |
PRA 02 | Thu 12-15 | Sept 26 | Oct 10 | Oct 24 | Nov 7 | Nov 21 |
PRA 03 | Fri 15-18 | Sept 20 | Oct 18 | Nov 1 | Nov 15 | Nov 29 |
PRA 04 | Fri 15-18 | Sept 27 | Oct 11 | Oct 25 | Nov 8 | Nov 22 |
PRA 05 | Mon 15-18 | Sept 23 | Oct 21 | Nov 4 | Nov 18 | Dec 2 |
PRA 06 | Mon 15-18 | Sept 16 | Sept 30 | Oct 28 | Nov 11 | Nov 25 |
PRA 07 | Wed 12-15 | Sept 25 | Oct 9 | Nov 6 | Nov 20 | Dec 4 |
PRA 08 | Wed 12-15 | Sept 18 | Oct 2 | Oct 16 | Nov 13 | Nov 27 |
Labs | 20% | Includes preparation, lab work, and report |
Homework | 5% | |
Midterm | 25% | Wednesday, October 30, 6-8pm |
Final Exam | 50% | TBA |