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This is the homepage for ME/CDS/EE 234(a,b) (Advanced Robotics) for Winter/Spring 2021/2022.

Course Staff, Hours, Location

Position Name Office Office Hours (changing weekly) Email Phone
Instructor Joel Burdick 245 Gates-Thomas send mail for an appointment jwb at robotics dot caltech dot edu 626-395-4139
Teaching Asst. Anushri Dixit 205 Gates-Thomas TBD adixit at caltech dot edu 626-395-????
Administrative Sonya Lincoln 250 Gates-Thomas 7:30am-noon; 1:00pm-4:30pm lincolns at caltech dot edu 626-395-3385
  • Lecture Schedule: TBD

Announcements For ME/CDS/EE 234(a)

  • 01/04/22: An Overview of the course was discussed in class.

Course Text and References

ME/CDS/EE 234(a): The first quarter will use two main text books:

Course Description

ME/CDS/EE 234(a) is devoted to an advanced treatment of robot kinematics. We will review rigid body kinematics, with an emphasis on a Lie-algebraic framework. Then the basic robot mechanisms are analyzed using these methods. The second half of the quarter will introduce the kinematics of robotic grasping and manipulation.

ME/CDS/EE 234(b) is devoted to robotic motion planning. The first half of the quarter will summarize several frameworks and algorithms for robotic motion planning, with an emphasis on incorporating uncertainty into the motion planning process. The second half of the quarter will take a deep dive into one particular motion planning problem: sensory robotic coverage planning. In sensory coverage planning, a robot must plan its motions so that its onboard sensors cover every point in a given environment, at least once.

Prerequisites: ME 133(a,b) or equivalent.

An overview of the course, including course mechanics, grading, etc. The most salient information is repeated below.


The final grade will be based on homework sets, and a final exam or final project. Covid permitting, we aim to have a few laboratory experiments, whose grades will be weighted as two homework exercises.

  • Homework (70%): Homework sets will be handed out every 7-10 days, and are due at 5 pm on the due date (which will always coincide with a class meeting). Homeworks can be dropped off in class (when in-person classes resume), or delivered to room 250 of Gates-Thomas (the office of Sonya Lincoln). Some homeworks will require computation. MATLAB or Mathematica should be sufficient to solve every homework posed in this course, though students can choose their favorite programming language. Code is considered part of your solution and should be included with the problem set when appropriate.
  • Final exam/project (30%): Students have the option to take a final exam (a limited time take-home format exam which is open book, open note, and computer allowed) or select a final project. The final project must incorporate some aspect of the course, and the topic and scope my be approved by the course instructor. The final exam will due at 5:00 pm the last day of finals. The final project is similarly due at 5:00 pm on the last day of finals.
  • Late Homework Policy: Students may automatically take a 2-day extension on two homeworks during each quarter.

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you must cite any use of material from outside references. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter. Computer code and graphical plots are considered part of your solution, and therefore should be done individually (you can share ideas, but not code). No collaboration is allowed on the examinations.

Course Schedule for ME115(b)

Week Date Topic Reading Optional Reading Homework

From Manipulator Singularities to Closed Loop Mechanisms

28 March (M) Manipulator Singularities (concluded)
Intro to Closed Loop Mechanisms
-N/A- -N/A- Homework 1
Solution 1
30 March (W) Closed Loop Linkages: Structure Equations & Mobility Murray, Li Sastry (MLS), Section 3.4 -N/A-
1 April (F) Closed Loop Linkages: Special Configurations Murray, Li Sastry (MLS), Section 3.4 -N/A-

Closed Loop Mechanisms and Parallel Mechanisms

4 April (M) Closed Loop Linkages: Multi-Loop Linkages MLS, Section 3.5 -N/A- -No Homework-
6 April (W) Intro to Parallel Linkages -N/A- -N/A-
8 April (F) Parallel Mechanisms: structure Equations and Singularities MLS Section 3.5

Parallel Mechanisms to Redundant manipulators

11 April (M) The Delta Mechanism Paper on Delta Kinematics History of Delta Mechanism; Singularities of Delta Mechanisms; Homework 2
Solution #2
13 April (W) Redundant Mechanisms and PseudoInverse -N/A-
15 April (F) Redundancy resolution and trajectory planning Notes on the Moore-Penrose Pseudo Inverse -N/A-

From Redundant Manipulators to Grasping

18 April (M) The Moore-Penrose Pseudo Inverse and SVD MLS Chapt 3, Section 5.1
20 April (W) Redundancy Resolution and Obstacle Avoidance Example
Intro to Grasping
MLS Chapt 3, Section 5.1 Maciejewski & Klein
22 April (F) Contact Models Section 5.2 of the MLS Text -N/A-

Force Closure Grasps

25 April (M) Finger Contact Models Section 2.1 of MLS Chapter5 -N/A- Homework 3
Solution 3
27 April (W) The Grasp Map
Secure Multi-Fingered Grasps
Section 2.2 of MLS Chapter 5 N/A-
29 April (F) Force Closure (continued) Section 5.3, 5.4 of the MLS Text -N/A-

Force Closure Grasps

2 May (M) Frictionless Force Closure -N/A- -N/A- Homework 4;
Solution 4
4 May (W) Force Closure and Internal Forces -N/A- -N/A-
6 May (F) Number of required fingers Section 5.4 of the MLS Text -N/A-

Yet more Robotic Grasping

9 May (M) Number of fingers needed to grasp an object Section 5.4 of MLS Text -N/A- Homework 5;
Solution 5
11 May (W) Grasp Planning/Hand Kinematics Section 5.5 of MLS Text -N/A-
13 May (F) Hand Kinematics Section 5.5 of the MLS Text -N/A-

Yet more Robotic Grasping

16 May (M) Differential Geometry of Curves Section 5.6 of MLS text
Notes on the Differential Geometry of Curves
-N/A- Homework #6
18 May (W) Planar Contact Equations Section 5.6 of MLS Text
Notes on the Planar Contact Equations
20 May (F) No Class due to travel -N/A- -N/A-


23 May (M) Review of planar contact equations
Grasp Equations with non-point fingers
Chapter 5 of MLS
25 May (W) Gears,Quasistatic Locomotion Slides on Gears -N/A-
27 May (F) No Class (travel) -N/A- -N/A-


30 May (M) Institute Holiday
1 June (W) Quasistatic Locomotion and Whole Body Manipulation Slides on Whole Body Manipulation -N/A-

Course Schedule for ME115(a)

Week Date Topic Reading Optional Reading Homework
Introduction and Review of Rigid Body Kinematics
4 Jan (Mon.) Class Overview Course Overview,
Chapter 1 of MLS
History of Kinematics Through 1900 (Introductory chapter from Kinematic Synthesis of Linkages) -No Homework-
6 Jan (W) Planar Rigid Body Kinematics,
Planar displacements
MLS Ch 2.1, Pages 19-23 -N/A-
8 Jan (F) Planar Rigid Body Displacements (continued),
Displacement groups
MLS Ch 2.1, -N/A-
From Planar Rigid Body Kinematics to Spherical Kinematics
11 Jan (M) Displacement groups, poles
Planar Displacements (PowerPoint)
-N/A- Homework 1,
Solution 1
13 Jan (W) Centrodes: Ellliptical Trammel,
Trammel, V 1, V 2, compliation

Intro to Spherical Kinematics

MLS Pages 22-26,
Notes on the Elliptical Trammel,
Archemides Trammel (Wikipedia)
Polyhedral Linkages Synthesized Using Cardan Motion Along Radial Lines
15 Jan (F) Spherical Kinematics (continued),
Classical Matrix Groups
MLS Ch 2.2, 2.3,
Notes on the Classical Matrix Groups
Spherical Kinematics
18 Jan (M) No Class: Marin Luther King Holiday -N/A- -N/A- No Homework
20 Jan (W) Cayley's Theorem,
MLS 27-31,
Notes on Rotations
22 Jan (F) No Class MLS 31-34 -N/A-
Spherical Kinematics (continued)
25 Jan (M) Angle/Axis Representation and Rodriguez Formula MLS 34-39 Notes on Algebras -N/A-
27 Jan (W) No Class -N/A- -N/A-
29 Jan (W) No Class -N/A- -N/A-
Spatial Kinematics
1 Feb (M) No Class -N/A- -N/A- Homework 2,
Solution 2
3 Feb (W) Exponential Coordinates and Euler Angles MLS Ch 2.2, 2.3 -N/A-
5 Feb (F) Quaternions MLS Pages 51-52 -N/A-
Spatial Kinematics (continued)
8 Feb (M) Quaternions (continued),
Intro to Spatial Kinematics
MLS 34-39 Notes on Algebras Homework 3,
Solution 3
8 Feb (M) Spatial Displacments,
Chasle's Theorem, Exponential Coordinates
MLS Pages 35-50 -N/A-
10 Feb (W) Motion Capture
Rigid Body Velocities
MLS Pages 51-61; Rodriguez' Displacement Equation; -N/A-
12 Feb (F) No Class -N/A- -N/A-

Spatial Kinematics: Velocities and Wrenches
15 Feb (M) No Class: President's Day Holiday MLS Ch 2.3; -N/A- Homework 4,
Solution 4
17 Feb (W) Rigid Body Velocities (continued) MLS Ch 2.3 -N/A-
19 Feb(F) Transformation of Velocities
Wrenches and Poinsot's Theorem
MLS Ch 2.4-2.5 -N/A-
Robot Manipulators
22 Feb (M) Wrenches (continued),
Screw Theory
-N/A- -N/A- No Homework
22 Feb (M) Robot Manipulators: Introduction MLS Chapter 3, pages 81-94 -N/A-
23 Feb (W) Denavit Hartenberg Convention MLS Chapter 3, pages 81-94 -N/A-
25 Feb(F) Forward Kinematics via the Denavit-Hartenberg Convention MLS Ch 3, DH-Parameters (from Wikipedia),
Scan from Craig Book on D-H Parameters
Forward/Inverse Kinematics
29 Feb (M) Denavit-Hartenberg Convention (continued), Examples MLS Ch 3; Rodriguez' Displacement Equation; -N/A- Homework 5,
Solution 5
2 Mar (W) Product of Exponentials Formula MLS Ch 3 -N/A-
4 Mar(F) Inverse Kinematics MLS Ch 3 -N/A-
Jacobian Matrix and Singularities
7 Mar (M) Manipulator Jacobian Matrices MLS Ch 3, pages 115-120; -N/A- Optional Homework 6
7 Mar (M) Jacobian Matrix (continued), End-effector forces MLS Ch 3, 121-123; -N/A-
9 Mar (W) Manipulator Singularities MLS Ch 3, pp 123-127 -N/A-