Dynamics of Robotic Systems
Course Summary: Motion planning and control of articulated dynamic systems: nonlinear joint control, experiments in joint control and multiaxis coordination, multibody dynamics, trajectory planning, motion optimization, dynamic performance and manipulator design, kinematic redundancies, motion planning of manipulators in space, obstacle avoidance.
Recommended preparation: courses 155, 171A, 263A,
Assignments & Grading:
HW Assignments  Problem Sets 20%
Paper Review 5%
Mid Term Exam (Take Home) 30%
Final Exam (Take Home) 40%
Participation 5%
Textbook:
(*) John Craig, Introduction to Robotics: Mechanism & Control, 4ed Edition, Addison Wesley 2018
(*) LungWen Tsai, Robotic Analysis, Wiley 1999,
Ch. 9, Dynamics of Serial Manipulators
(*) Matjaž Mihelj, Tadej Bajd, Aleš Ude, Jadran Lenarčič, Aleš Stanovnik, Marko Munih, Jure Rejc, Sebastjan Šlajpah, Robotics, Springer 2019
Chapter 10: Robot Control
Class Notes
Class 01A: Introduction & Basic Ideas
Class 02A: Special Description & Transformation (Review)
Class Supplement: Equivalent angle axis vector
Class 03A: Direct Manipulator Kinematics (Review)
Class 04A: Inverse Manipulator Kinematics (Review)
Class 05A: Jacobian: Velocities and Forces (1/4)
Class 06A: Linear and Angular Velocities (2/4)
Class 07A: Velocity propagation (3/4)
Class 08A: Jacobian: Velocity propagation (4/4)
Class 09A: Manipulator Dynamics (1/4)
Class 10A: Manipulator Dynamics (2/4)
Class 11A: Manipulator Dynamics (3/4)
Class 12A: Manipulator Dynamics (4/4)
Class 13A: Trajectory Generation (1/2)
Class 14A: Trajectory Generation (2/2)
Class 15A: Intro to Control
Section Notes (TA)
Section 01: Forward & Inverse Kinematics (Yasukawa Motoman L3)
Section 02: Robotics  Matlab ToolBox (Matlab Example  XML )
Section 03: Jacobian  Velocity Propagation Direct Diff (SCARA)
Section 04: Jacobian  Force Propagation (SCARA)
Section 05: x
Section 06: x
Section 07: x
Section 08: x
Section 09: x
Homework
Week 
Homework 
Due Date 
W1 
HW 0  Presentataion
Review three journal papers (1 journal paper = 2 conference paper) or 6 conference papers or any other combinations of both related to the content of one of the topics thought in class (i.e. Serial/Parallel Robotic Arm, Direct/Inverse Kinematics, Jacobian, Dynamics, Trajectory Generation, Control). Give a 10 min presentation in class of a robotic system or an algorithm including the following content:
Outline of the Presentation
(*) Algorithm based presentation
Define the problem
Define the solution
Describe the Algorithm
Describe numerical / analytical problems
Realtime / offline
Web Site
Link the content of the paper to one of the topics taught in class.
List the references.
(*) Robotic System based presentation
Name
Application
Physical Dimensions (Height, Length ,Weight)
Sensors & Actuators
Power Source
Control Algorithms
Cost Project
Status
Web Site
Link the content of the paper to one of the topics taught in class.
List the references.
Journals
IEEE Transactions on Robotics
IEEE Transactions on Automation
IEEE / ASME Transactions on Mechatronics
The International Journal of Robotics Research
Journal of Field Robotics
Journal of Intelligent and Robotic Systems
Robotica
Robotics and Autonomous Systems
Confrances
ICRA
IROS
Biorob 
W2W10 
W2 
HW 1  DH Parameters & Direct Kinematics
Robotic Arms Libraray
Note:
HW is applicable to ALL of the robotic arms in the library
Define the DH Parameters of the robotic systems in the library in two methods
(a) modified form as discussed in class
(b) standard form
Solutions
HW 1 Solution PDF
HW 1 Solution PDF (MATLAB)
HW 1 Solution (MFile)
HW 1 Solution (MFile  HTML)

W3
Fri 
W3 
HW 2  DH Parameters & Direct Kinematics
Robotic Arms Libraray
Note:
HW2 is applicable to subset of the robotic arms in the library including:
3D1RRR
3D4RRR (Spherical Wrist)
3D6RRPRRR (Stanford Arm)
3D6PPPRRR
1. Define the homogeneous transformation matrixes (modified form only)
2. Derive the Direct Kinematics explicitly / analytically and defining the homogeneous transformation matrix (base to tool) – You may use Matlab to do so. In this case, use the Matlab output and rewrite the result in a simplified version (i.e. sum/diff of angles)
4. Using the Matlab’s Robotic toolbox plot the figures of all the robotic systems in the library
For Illustrations only you may use the following values as needed:
a_i=0.3m
d_i=0.1m
5. Submit the Matlab source code along with your solution
Solutions
HW 2 Solution PDF 
W5
Mon 
W4 
HW 3  Inverse Kinematics
Robotic Arms Libraray
Note:
HW4 is applicable to subset of the robotic arms in the library including:
3D1RRR
3D4RRR (Spherical Wrist)  Use only analytical approach
3D6RRPRRR (Stanford Arm)
3D6PPPRRR
1. Derive the Inverse Kinematics of each robotic arm in the library using two methods:
(a) Geometric Approach (excluding the Spherical Wrist)
Notes:
(*) For 6 DOF robots use hybrid approach
(*) Divided the problem into a position problem (frame 0 to frame 4) that is solved base on geometric considerations and a orientation problem (frame 4 to frame 6) that is solved analytically (for example ZYZ configuration of the wrist  See notes)
(*) Pay attention to the way the homogeneous transformation matrix from frame 3 to frame 4 is divided between the two problems
(b) Analytical Approach.
Notes
(*) Define an expression for each DOF.
(*) Each angle must be define using the function Atan2(*)
Note For both methods:
(*) Use the original parameters (No numerical values) in your derivations
2.
Sketch / Explain the multiple solutions.
Use the follwoing parameters For simulation purposes
3D6PPPRRR
d1 = 0.1 m (offset 0.01 m)
d2 = 0.1 m (offset 0.01 m)
d3 = 0.1 cm (offset 0.01m)
d4 = 0.1 m
a3= 0.02 m
L_T1 = 0.07 m
L_T2 = 0.03 m
L_T3 = 0.01 m
L_S = 0.01 m
Solution
HW 3 Solution

W6
Mon 
W5 
HW 4  Jacobian
Robotic Arms Libraray
Note:
HW5 is applicable to subset of the robotic arms in the library including:
3D1RRR
3D4RRR (Spherical Wrist)
3D6RRPRRR (Stanford Arm)
3D6PPPRRR
1. Derive the Jacobian matrix for each robotic arm using the following method and expressed them all in frame 0. Note that once the Jacobian is expressed in the same frame (e.g. Frame 0) the expression is the same regardless of the method used to derive it.
(*) Velocity Propagation (Expressed in Frame N)
2. Calculate the determinate of the Jacobian and define the singular configurations of each arm. Note that there might be more than on singular configuration.
3.
Sketch the singular configurations.
4. For the RRR arm in the libraray draw the linear and angular velocities similar to the example shown in class.
Solutions
HW 4 Solution 
W7
Mon 
W6 
HW 5  Jacobian
Robotic Arms Libraray
Note:
HW5 is applicable to subset of the robotic arms in the library including:
3D1RRR
3D4RRR (Spherical Wrist)
3D6RRPRRR (Stanford Arm)
3D6PPPRRR
1. Derive the Jacobian matrix for each robotic arm using following methods and expressed them all in frame 0. Note that once the Jacobian is expressed in the same frame (e.g. Frame 0) the expression is the same regardless of the method used to derive it.
(*) Direct Derivative (Expressed in Frame 0)
(*) Force Propagation (Expressed in 0).
Solutions
HW 5 Solution 
W8
Mon 
W7 
HW 6  Dynamics
For the versions of the 2 DOF arm (2D1RR) presented in class derive the equations of motion using the alternative method. For the first version in which the CM is located in the joints use the Lagrange method. For the second version in which the CM is located in the middle of the link use the NewtonEuler method.
For the Manipulator 3D1RRR derive the equations of motion using the two methods. Assume that the CM for each link is Lci units of length from the joint.
Solutions
HW 6 Solution

W9
Mon 
W8 
HW 7  Trajectory Generation
TBD
Solutions
HW 7 Solution

W9
Fri 
W9 
HW 8  Parallel Manipulators
TBD
Solutions
HW 8 Solution

W10
Fri 
W10 
HW 9  Control
TBD
Solutions
HW 9 Solution 

Labs (Denso Robotic Arms)
Lab 0
Lab 1
Lab 2
Lab 3
Lab 4
Exams (Take Home)
Midterm Exam  Take Home  Due Week 11 (Monday at 6:00)
Final Exam
 Take Home  Due Week 12 (Monday at 6:00)
Matlab
Robotic Toolbox  Free (by Corke)
Robotics Toolbox (Release 10)
Introduction to Robotics Toolbox for MATLAB (Powerpoint Slides  TA)
The book Robotics, Vision & Control, Second Edition (Corke, 2017) is a detailed introduction to mobile robotics, navigation, localization; and arm robot kinematics, Jacobians and dynamics illustrated using the Robotics Toolbox for MATLAB (Availble online to UCLA Students)
Matlab Code (Robotic Toolbox)
Puma 560 (Modified DH)  StdMod_puma560.m
Robotic Toolbox (by Mathworks)
Matlab Demo
Robot Manipulation, Part 1: Kinematics
Robot Manipulation, Part 2: Dynamics and Control
Trajectory Planning for Robot Manipulators
Mathematica Demos (Robotics)
Note: A viewer is required for running the demos off line
Special Description & Transformation
Randomize Motion for Six Degrees of Freedom
Mathematica Demo
Robot Manipulator Workspaces
YouTube Explanation
Mathematica Demo
DenavitHartenberg Parameters for a ThreeLink Robot
Mathematica Demo
Common Robot Arm Configurations
YouTube Explanation
Mathematica Demo
Forward and Inverse Kinematics
Model of an Industrial Robot Arm
YouTube Explanation
Mathematica Demo
Inverse Kinematics for a Robot Manipulator with 6 DOF
YouTube Explanation
Mathematica Demo
Forward Kinematics
YouTube Explanation
Mathematica Demo
Inverse Kinematics
YouTube Explanation
Mathematica Demo
Forward and Inverse Kinematics of the SCARA Robot
YouTube Explanation
Mathematica Demo
A Model of the SCARA Robott
YouTube Explanation
Mathematica Demo
Kinematics of SCARA Robot in 2D
YouTube Explanation
Mathematica Demo
Kinematics of a Redundant Anthropomorphic Arm with 7 DOF
YouTube Explanation
Mathematica Demo
Inverse Kinematics in Redundant Robot Manipulator (Swivel Angle)
YouTube Explanation
Mathematica Demo
Manipulability
Forward and Inverse Kinematics for TwoLink Arm
YouTube Explanation
Mathematica Demo
Manipulability Ellipsoid of a Robot Arm
YouTube Explanation
Mathematica Demo
Trajectory Planning
Trajectory Planning of Robot for Painting Art
YouTube Explanation
Mathematica Demo
Autolev
Class Notes: Introduction to Autolev
Class Video (1/2)  Introduction  Example (3R)
Class Video (2/2)  Example  Industrial Robot (6R)
Autolev Code (Zip)
Industrial Robotic Arms  Companies
Expo 21XX  Generic List
Denso Robotics (*,+)
KUKA (*,+)
Motoman (+)
Staubli (*,+)
FANUC (+)
Adept (*,+)
ABB (*,+)
Mitsubishi (+)
Kawasaki (+)
Epson (*,+)
Notes
(*) CAD files are available online
(+) Data sheet / Specs / Schematic drawings are available online
Videos (YouTube)
DenavitHartenberg Reference Frame Layout
