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A student may pursue an M.S. with a thesis or non-thesis option. The minimum number of credits is 30. Three courses are required, plus an additional three courses from a restricted selection. Two additional 6000-level or higher courses (not including independent study, seminars, or thesis) from any department are required. Remaining credits to fill the 30-credit minimum may be chosen from other 6000-level courses or from independent study, seminars, or thesis credits. 

Students in the Mechanical Engineering M.S. Robotics Track must satisfy departmental degree requirements as well, which in addition to the track requirements includes:

• A minimum of two 7000 level ME courses (six credits)

• 12 credit hours of ME courses. 

A sample program of study meeting these requirements for a thesis M.S. student is shown below, Table 1.  Please refer to the ME Graduate Advising Guide for specific details of ME graduate degree requirements.  Please contact Candace Christensen if you have questions about specific ME degree requirements.  For more information about the ME Robotics Track and Admission, please contact Mark Minor (minor 'at' mech.utah.edu) or John Hollerbach (jmh 'at' cs.utah.edu).

Required Courses

CS 6310/ME 6220 Introduction to Robotics (3,F). John Hollerbach, instructor. Prereq: CS 1000, MATH 2250, PHYCS 2220.



The mechanics of robots, comprising kinematics, dynamics, and trajectories. Planar, spherical, and spatial transformations and displacements. Representing orientation: Euler angles, angle-axis, and quaternions. Velocity and acceleration: the Jacobian and screw theory. Inverse kinematics: solvability and singularities. Trajectory planning: joint interpolation and Cartesian trajectories. Statics of serial chain mechanisms. Inertial parameters, Newton-Euler equations, D'Alembert's principle. Recursive forward and inverse dynamics.



ME 6960 Introduction to Robot Control (3,S). Mark Minor, instructor.
Prereq: CS 6310/ME 6220.



Control of manipulation and mobile robots is studied. Topics include control system fundamentals, sensors and actuators, characterization and control of manipulators, and basic characterization and control of mobile robots. Projects provide hands-on experience controlling a basic serial manipulator and a mobile robot.



CS 6370 Geometric Computation for Motion Planning (3,F). David Johnson, instructor. Prereq: CS 1020, MATH 2250.



Geometric computation is the study of practical algorithms for solving queries about geometric properties of computer models and relationships between computer models. Robot motion planning uses these algorithms to formulate safe motion through a modeled environment. In addition, algorithms for geometric computation are used in computer animation, simulation, computer-aided design, haptics, and virtual reality. Topics to be covered in this course are spatial subdivision and model hierarchies, model intersection, distance queries and distance fields, medial axis computations, configuration space, and motion planning. The course will rely on lectures, readings, and projects to provide understanding of current practices in the field.

• Perception.
  
  

  CS 6320 Computer Vision (3,S). Tom Henderson, instructor. Prereq: CS 3510, MATH 2210, MATH 2270.
  
  

  Basic pattern-recognition and image-analysis techniques, low-level representation, intrinsic images, ``shape from'' methods, segmentation, texture and motion analysis, and representation of 2-D and 3-D shape.
  
  

  CS 6964 Image Processing for Graphics and Vision (3,S). Ross Whitaker, instructor. Prereq: Programming, data structures, linear algebra, calculus.
  
  

  This is an introductory course in processing grey-scale and color images --- taught at the senior/grad level. This course will cover both mathematical funadmentals and implementation. It will introduce students to the basic principles of processing digital signals and how those principles apply to images. These fundamentals will include sampling theory, transforms, and filtering. The course will also cover a series of basic image-processing problems including enhancement, reconstruction, segmentation, feature detection, and compression. Assignments will include several projects with software implementations and analysis of real data.

  
  
• Cognition.
  
  

  CS 6300 Artificial Intelligence (3,S). Prereq: CS 3510.
  
  

  Introduction to the field of artificial intelligence, including heuristic programming, problem-solving, search, theorem proving, question answering, machine learning, pattern recognition, game playing, robotics, computer vision.
  
  

  CS 6350 Machine Learning (3,F). Prereq: CS 3510. CS 5300/6300 recommended.
  
  

  Techniques for developing computer systems that can acquire new knowledge automatically or adapt their behavior over time. Topics include concept learning, decision trees, evaluation functions, clustering methods, explanation-based learning, language learning, cognitive learning architectures, connectionist methods, reinforcement learning, genetic algorithms, hybrid methods, and discovery.
  
  

  CS 6330 Multiagent Systems (3,S). Tom Henderson, instructor. Prereq: Knowledge of programming, data structures, processes, language syntax, Matlab or C.
  
  

  Covers fundamental notions of (1) software agents, including: autonomy, communication, persistence, and intelligence; and (2) multiagent systems, including: communication standards, cooperation, competition and coordination. Methods will be applied to a practical application (usually in Matlab or C).

  
  
• Action.

  
  

  CS 7360 Virtual Reality (3,S). Pete Willemsen, instructor. Prereq: CS 6310/ME 6220.
  
  

  Human interfaces: visual, auditory, haptic, and locomotory displays; position tracking and mapping. Computer hardware and software for the generation of virtual environments. Networking and communications. Telerobotics: remote manipulators and vehicles, low-level control, supervisory control, and real-time architectures. Applications: manufacturing, medicine, hazardous environments, and training.
  
  

  CS 7310/ME 7230 Advanced Manipulation and Locomotion (3,S) Instructor: Mark Minor. Prereq: CS 6310/ME 6220.
  
  

  This course will examine grasping, rolling, and sliding manipulation from two perspectives; (1) manipulating the pose of an object with an end-effector via grasping, rolling, and sliding manipulation, and, (2) manipulating the trajectory of a mobile robot via the rolling and sliding contact of wheels, feet, or curved exoskeletons and the ground.
  
  

  CS 7370 System Identification for Robotics (3,S). John Hollerbach, instructor. Prereq: CS 6310/ME 6220.
  
  

  Modeling and identification of the mechanical properties of robots and their environments. Review of probability and statistics. Parametric versus nonparametric estimation. Linear least squares parameter estimation, total least squares, and Kalman filters. Nonlinear estimation and extended Kalman filters. State estimation. Specific identification methods for kinematic calibration, inertial parameter estimation, and joint friction modeling.

Elective Courses

With approval of the supervisory committee, a student will take two elective courses at a 6000 level or higher from any department, excluding independent study, seminars, research credit, and required courses.  Again, remember that ME students must also satisfy ME Graduate Degree requirements.

Depending on whether a student is pursuing a thesis or non-thesis M.S., additional 6000-level or higher courses can be chosen, this time including independent study, seminars, and research credit, in order to reach a 30-credit minimum.

Table 1.  Example Program of Study for a ME Robotics Track M.S. Student (Thesis Option)