ECE 470 – AE 482 – ME 445: Introduction to Robotics (Spring 2019)

Teaching Staff

Meeting times

The class meets Tuesday and Thursday 12:30PM to 1:50PM in ECEB 1015.

The class counts for 4 credits, and includes a lab

Instructor’s Office Hours: Tuesday 2-3pm in CSL 166 or by appointment.

TA’s Office Hours:

Location: ECEB 3071 [lab]

Times: Yu Chen: Monday 11AM-12PM    Ben Walt: Wednesday 1PM-2PM   Peixin Chang: Wednesday 3PM-4PM

We are on Piazza


  • There will be almost weekly homeworks assigned (no homeworks due on the midterm weeks). Unless otherwise specified, the homeworks are due a week from the day they are assigned.
  • The homework will be assigned mostly from the main textbook, so make sure to have access to it early (alternatively, it is on reserve in the Grainger library)
  • Homeworks are due in HW Box 90 in the ECE Building by 2pm (end of class) of the due date


HW1 (assigned Tuesday Jan 22, due Friday Feb 1): Do the following exercises from the textbook: 2.5; 2.9(a,b only); 2.11(a,b only),  3.1 (a through g included only), 3.4. Note: we will cover the material for 3.1 on Thursday Jan 24. Solution

HW2 (assigned Thu Jan 31, due Thu Feb 7): Do the following exercises from the textbook: 3.6, 3.17, 3.20, 3.27, 3.28. Note for Prob. 3.20: In the book, the frame used in Prob 3.20 are left-handed. We do not want to use them. Swap the z and x axes and use the resulting frame instead (which is right-handed). Solution

HW3 (assigned Thu Feb 7, due Thu Feb 14): Do the following exercises from the textbook: 3.16 (30pts), 3 .27 (10pts), 3.31 (10pts), 4.2 (20pts, You can skip the software part. Only derive the S_i and B_i as done in class), 4.15 (20pts, you can assume that the pitch of the first joint is h, only S_i, no B_i) Solution

HW4 (assigned Thu Feb 14, due Thu Feb 21): Do the following exercises from the textbook: 4.2 (derive the B’s), 4.15 (derive the B’s), 4.7 (20pts), 4.9 (20pts). Solution

HW5 (assigned Thu Feb 2, due Thu Feb 28): Do the following exercises from the textbook: 3.31(10pts) , 5.8 (20pts), 5.11 (40 points). Solution

(No HW due March 7, read the Note on computing Jacobians.)

HW6 (assigned Thu Apr 4, due Thur Apr 11) Do the following exercises from the textbook: 8.2 (30pts), 8.4 (70 pts, you can omit part b). Solution

HW7 (assigned Thu Apr 11, due Thu Apr 18) Do the following exercises from the textbook: 9.1 (10pts), 9.2 (15pts), 9.4 (15pts) and 11.2 (10pts). Solution

HW8 (assigned Tue Apr 16, due Tue Apr 30). Do the following exercises from the textbook:  11.3 (15pts), 11.4 (15pts) and 11.5 (20pts). Solution

The Final grade will be evaluated according to:

Homeworks:        15%
Labs:             20%
Exam 1:           17.5% [Mar 14] Exam Info
Exam 2:           17.5% [Apr 25] Exam Info
Final:            30% [May 10] Exam Info


  • Textbook: Modern Robotics: mechanics, planning and control, by K. Lynch and F. Park (Cambridge University Press)
  • Recommended reference:  Robot Modelling and Control, by M. Spong, S. Hutchinson and M Vidyasagar (Wiley and Sons, 2005)
  • Note on computing Jacobians


A good understanding of linear algebra and calculus. The official prerequisites are:  Credit in MATH 225 or MATH 286 or MATH 415 or MATH 418.

Tentative Lecture Schedule

The lecture schedule below is tentative. It will be updated after each lecture to reflect what was covered and what we intend to cover in the next lectures. The slides will also be updated, so check often to have the latest version.

Note: If you cannot access the slides, please follow this link. Use the helpdesk, whose contact info is at the bottom, if necessary.


Date Topic Assignments  
Jan 17 (X) General introduction and overview of the course.
Configuration space: Degrees of Freedom. Slides
Read Chap. 1. Chap. 2.1-2.2
Jan 22 (X) Configuration Space topology, holonomic and non-holonomic constraints. Slides  [updated 2019] Read Chap. 2.3-2.5
Jan 24 (X) Rigid-Body Motions: rotation matrices and homogeneous transformations in 2D and 3D. Slides [updated 2019] Read 3.1-3.3
Jan 29 (X) Exponential Coordinates and logarithm for rotation in 3D and Homogenous transformations in 3D Slides [Updated 1/29] Read 3.3-3.4
Jan 31 (X) Homogenous transformations, angular velocities and twists. Slides [Updated 2019]

Sir Ball Treatise on Screw Theory (for the curious only; shows you how this material was discussed circa 1876)

Feb 5 (X) Screw motions and their twists Slides [2019]
Feb 7 (X) Forward Kinematics: Product of Exponentials formula Slides Read 4.0-4.1
Feb 12 (X) Forward kinematics: Changing frames in PoE and  Denavit-Hartemberg formalism Slides Read Appendix C
Feb 14 (-) Velocity kinematics: Jacobians Slides Read 5.1
Feb 19 Velocity Kinematics: Jacobians and singular configurations Slides Read 5.2-5.7
Feb 21 Inverse kinematics: Analytic Approach Slides Read 6.1-6.2
Feb 26 Inverse kinematics: numerical approach; inverse velocity kinematics Slides (updated Oct 10) Read 6.3-6.6
Feb 28 Kinematics of closed chains Slides Read 7.1-7.2
Mar 5 Dynamics: Lagrangian formulation Slides Read 8.1-8.2
Mar 7 Dynamics: single rigid-body Slides Read 8.2
Mar 12 Review
Mar 14 Exam 1 [In class]
Spring Break
Mar 26 Dynamics: Newton-Euler Inverse dynamics and forward dynamics of open chains Slides Read 8.3
Mar 28 Dynamics: closed form and an example Slides Read 8.3-8.4
Apr 2 Trajectory generation Slides Read 9.1-9.3
Apr 4 Q&A and midterm 1 solutions Read 11.1-11.4
Apr 9 Trajectory generation Slides Read 11.1-11.3
Apr 11 Robot Control Slides Read 11.3
Apr 16 Robot Control: Velocity inputs Slides

Robot Control: Torque/force inputs Slides

Read 11.4
Apr 18 No Lecture: extended office hours.
Apr 23 Review session: correction of sample exam 2
Apr 25 Exam 2 [In class]
Apr 30 Exam 2 solution and Q&A