24-760 Special Topics: Robot Dynamics and Analysis

Meeting Times: Tu/Th 2:00-3:50pm
Meeting Location: Baker Hall A36
Semester: Fall, Year: 2024
Units: 12

Instructor information

Name: Prof. Aaron M. Johnson
E-Mail: amj1@cmu.edu
Office location: Scaife B08
Office hours: TBD

Course Description

This course covers the dynamics of robotic systems with a focus on the mathematical structure of the dynamics and numerical analysis. Topics will start by reintroducing basic kinematics and dynamics in a more formal mathematical framework before moving on to contact conditions, friction, terramechanics, hybrid dynamical systems, timestepping simulation, and contact invariant optimization. After the course students will be able to write simulation and optimization methods for analyzing robotic systems. Students should have taken a prior course in dynamics, and be comfortable with linear algebra, multivariable calculus, and programming in Matlab.

Prerequisites

24-351 Dynamics OR 16-711 Kinematics, Dynamic Systems, and Control (or equivalent)
Comfortable programming in Matlab
Linear algebra, multivariable calculus, and differential equations

Learning Objectives

Increase formal understanding of rigid-body dynamics with contact.
Implement simulation and optimization algorithms to analyze robotic systems.
Read and understand technical articles on mechanics and robotic systems.
Ability to apply mathematics and engineering principles to solve problems found in robot design, control, and analysis.
Ability to disseminate engineering work to a broad professional community via written communication.

Textbook

No textbook is required for this class. Readings will be posted online and many will come from:

R. M. Murray, Z. Li, and S. S. Sastry. A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press, 1994. PDF.
A. M. Johnson, S. A. Burden, and D. E. Koditschek, "A hybrid systems model for simple manipulation and self-manipulation systems", The International Journal of Robotics Research, vol. 35, pp. 1354, 2016. PDF.
A. M. Johnson. Advanced Robot Dynamics. Online Textbook, 2021-- . Info

Assessments

The final course grade will be calculated using the following categories:

Assessment	Percentage of Final Grade
Homeworks	60
Exams	40

Lecture Topics

Preliminary list of class topics (see Canvas for detailed schedule, readings, etc):

Fundamentals:
- Topological spaces, maps, notation, tangent space, norms
- Implicit function thm, inverse function thm, constraints
Kinematics:
- Frames, rotations, velocities, twists, adjoint
- Forward & inverse kinematics, Jacobians
- Multi-finger/multi-leg kinematics
Dynamics:
- Lagrangian dynamics
- Constrained dynamics
- Manipulation dynamics
Contact:
- Contact dynamics, impact
- Complementarity
- Friction
- Collision detection
Hybrid Systems:
- Hybrid dynamical systems definitions
- Analysis of hybrid dynamics
Simulation & Optimization:
- Timestepping & hybrid simulation
- Shooting & direct colocation