MECH 672 - Navigation and Control of Robotic and Aerospace Systems

Modeling, navigation, and control of robotic and aerospace systems that rotate and translate in three-dimensional space. Kinematic and dynamic models. Nonlinear state-estimation strategies for navigation. Nonlinear control strategies.

Instructor: Prof. James Richard Forbes

Course Overview

MECH 672 introduces modern navigation and control methods for robotic and aerospace systems operating in three-dimensional space. The course emphasizes state estimation, navigation, modeling, and nonlinear control techniques that arise in robotics, aerospace engineering, autonomous systems, and related fields.

Topics include:

  • Probability theory and stochastic processes
  • Kinematic and dynamic system models
  • Matrix Lie groups
  • Kalman and extended Kalman filtering
  • Bayes filtering
  • Smoothing methods
  • Lyapunov stability theory
  • Nonlinear control design

Prerequisite and Corequisite Courses

There are no official prerequisite or corequisite courses. However, the following courses are beneficial:

  • MECH 412
  • MECH 513

Students are expected to be comfortable with:

  • Calculus
  • Differential equations
  • Linear algebra
  • Probability theory
  • Numerical methods

Python Resources

The course makes extensive use of Python together with NumPy and SciPy.

Useful resources:

Learning Outcomes

By the end of the course, students will be able to:

  • Model robotic and aerospace systems that rotate and translate in three dimensions.
  • Design and implement Kalman-filter-based navigation systems.
  • Formulate and solve a batch state estimation problem.
  • Apply nonlinear stability theory to engineering systems.
  • Design nonlinear controllers for robotic and aerospace applications.
  • Use modern computational tools to solve state-estimation and control problems.

Textbooks

There is no required textbook. However, lectures are based on the following references.

State Estimation/Navigation:

  • T. D. Barfoot, State Estimation for Robotics. New York, NY: Cambridge University Press, 2017.
  • J. A. Farrell, Aided Navigation: GPS with High Rate Sensors. McGraw-Hill Education, 2008.
  • Y. Bar-Shalom, X. R. Li, and K. Thiagalingam, Estimation with Applications to Tracking and Navigation. Hoboken, NJ: Wiley, 2001.
  • S. Särkkä and L. Svensson, Bayesian Filtering and Smoothing, 2nd ed. Cambridge, UK: Cambridge University Press, 2023.
  • A. J. Haug, Bayesian Estimation and Tracking: A Practical Guide. Hoboken, NJ: John Wiley & Sons, Inc., 2012.

Nonlinear Control:

  • H. Marquez, Nonlinear Control Systems. Hoboken, NJ: John Wiley & Sons, Inc., 2003.
  • M. Vidyasagar, Nonlinear Systems Analysis, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1993.
  • H. K. Khalil, Nonlinear Systems, 3rd ed. Pearson Prentice Hall, 2002.

Kinematics and Dynamics:

  • A. H. J. de Ruiter, C. J. Damaren, and J. R. Forbes, Spacecraft Dynamics and Control: An Introduction. West Sussex, UK: John Wiley & Sons, Ltd., 2013.
  • P. C. Hughes, Spacecraft Attitude Dynamics, 2nd ed. Mineola, NY: Dover, 2004.

Additional Resources

  • D. Simon, Optimal State Estimation. Hoboken, NJ: John Wiley & Sons, Inc., 2006.
  • J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynamic Systems, 2nd ed. Boca Raton, FL: CRC Press, 2012.
  • R. F. Stengel, Optimal Control and Estimation. New York, NY: Dover, 1994.

Schedule

Week Date Topic Materials
1 Sep/Jan Linear Algebra Review

Linear systems of equations, least squares, and matrix decompositions.
2 Sep/Jan Probability Theory Review

Probability density functions, marginalization, conditioning, and Bayes rule.
3 Sep/Jan Linear Systems

Linear state-space models, controllability, observability, and linearization.
4 Sep/Jan Stochastic Processes

White-noise driven systems, uncertainty propagation, and Allan variance analysis.
5 Oct/Feb Kinematics and Dynamics

Kinematic and dynamic models for rigid-body motion in three dimensions.
6 Oct/Feb Matrix Lie Groups

SO(2), SE(2), SO(3), SE(3), and uncertainty representations on Lie groups.
7 Oct/Feb The Kalman Filter

Derivation of the Kalman filter and applications to navigation.
8 Oct/Feb Extended Kalman Filters

EKF-based navigation, multiplicative EKF, invariant EKF, and matrix Lie group EKF formulations.
9 Nov/Mar The Bayes Filter

Bayes filter derivation, Kalman filtering as a special case, and sigma-point approximations.
10 Nov/Mar Batch State Estimation

MAP estimation, solving the MAP problem via Gauss-Newton optimization, the sliding window filter.
11 Nov/Mar Smoothing

Cholesky smoother and RTS smoothing.
12 Nov/Mar Nonlinear Stability Theory

Equilibrium points, Lyapunov stability, LaSalle’s invariant set theorem, and Barbalat’s lemma.
13 Dec/Apr Nonlinear Control

Nonlinear control design for robotic and aerospace systems.