Graduate Programs

Program Description

The Robotics program offers a graduate certificate and the degrees of Master of Science and Doctor of Philosophy in Robotics.  The graduate certificate is intended for working professionals. The non-thesis MS is designed to prepare candidates for industry careers in robotics. The thesis MS and PhD degrees are designed to prepare students for research careers.

The Robotics program also offers combined BS+MS degrees for Mines undergraduate students. These degrees offer an expedited graduate school application process and allow students to begin graduate coursework while still finishing their undergraduate degree requirements.

Program Details

Admission Requirements

MS and PhD

The minimum requirements for admission to the certificate program and MS and PhD degrees in Robotics are:

  • Applicants must have a Bachelor’s degree, or equivalent, from an accredited institution with a grade-point average of 3.0 or better on a 4.0 scale prior to matriculating into the Robotics degree program.
  • Students are expected to have completed the following coursework: (1) two semesters of calculus, (2) differential equations, and (3) data structures.  The Robotics graduate admissions committee may require that students who do not meet this expectation demonstrate competency or take remedial coursework.  Such coursework may not count toward the graduate degree. The committee will decide whether to recommend regular or provisional admission.
  • Graduate Record Examination (Quantitative section) score of 151 or higher (or 650 on the old scale). Applicants who have graduated with a computer science, engineering, or math degree from Mines within the past five years are not required to submit GRE scores.
  • TOEFL score of 79 or higher (or 550 for the paper-based test or 213 for the computer- based test) for applicants whose native language is not English. In lieu of a TOEFL score, and IELTS score of 6.5 or higher will be accepted.
  • For the PhD program, prior research experience is desired but not required.

Transfer Credit Graduate level courses taken at other universities for which a grade equivalent to a “B” or better was received will be considered for transfer credit with approval of the Advisor and/or Thesis Committee, and home department head, as appropriate. Transfer credits must not have been used as credit toward a Bachelor degree. For the MS degree, no more than nine credits may transfer. For the PhD degree, up to 24 credit hours of courses may be transferred. In lieu of transfer credit for individual courses, students who enter the PhD program with a thesis-based master’s degree from another institution may transfer up to 36 hours in recognition of the course work and research completed for that degree.

400-level Courses As stipulated by the Mines Graduate School, students may apply toward graduate degree requirements a maximum of nine (9.0) semester hours of department- approved 400-level course work.

 

Mines’ Combined Undergraduate / Graduate Degree Program

Current Mines undergraduate students are encouraged to apply for the combined program once they have taken five or more technical classes at Mines (classes transferred from other universities will not be considered). This requirement may be met by any 200-level or above course with a CSCI, MEGN, or EENG prefix, excluding field session and senior design courses.

Students enrolled in Mines’ Combined Undergraduate/Graduate Program (meaning uninterrupted registration from the time the student earns a Mines undergraduate degree to the time the student begins a Mines graduate degree) may double count up to six hours of credits which were used in fulfilling the requirements of their undergraduate degree at Mines, towards their graduate program. Any courses that count towards the graduate degree requirements as either “Required Coursework” or “Elective Coursework”, as defined below, may be used for the purposes of double counting at the discretion of the advisor (MS Non-Thesis) or thesis committee (MS Thesis or PhD). These courses must have been passed with a “B-” or better and meet all other University, Department, Division, and Program requirements for graduate credit.

Graduate Certificate in robotics

The graduate certificate requires 12 credit hours of coursework, as summarized in the table below. Please note: only 3 of the 12 credit hours can include coursework at the 400-level or lower to achieve the Graduate Certificate.

 

Robotics Core Four courses, one from each focus area’s core course list 12.0
Total Semester Hrs 12.0
Master of Science IN ROBOTICS

MS degrees will require 30 credit hours, with thesis options substituting for electives. 

MS Non-Thesis (MS-NT) 
Students must take 30 credit hours of coursework to complete the degree, as summarized in the table below.
 

Robotics Core (Breadth) Four courses, one from each focus area’s core course list 12.0
Robotics Electives (Depth) Two courses from electives course list 6.0
Technical Electives Four courses in any participating robotics department (CSCI, EENG, MEGN) 12.0
Total Semester Hrs 30.0

MS Thesis 
Students must take 21 credit hours of coursework and 9 credit hours of MS thesis research to complete the degree, as summarized in the table below. At the conclusion of the MS Thesis, the student must make a formal presentation and defense of their thesis research. A student must “pass” this defense to earn an MS degree. See the Robotics Graduate Catalog for more details about MS Thesis degree requirements.

Robotics Core (Breadth) Four courses, one from each focus area’s core course list 12.0
Robotics Electives (Depth) Two courses from electives course list 6.0
Technical Electives One course in any participating robotics department (CSCI, EENG, MEGN) 3.0
MEGN/CSCI/EENG 707 GRADUATE THESIS / DISSERTATION RESEARCH CREDIT 9.0
Total Semester Hrs 30.0
Doctor of Philosophy IN ROBOTICS

The Robotics PhD requires 36 credit hours of coursework, plus 36 research credit hours, as summarized in the table below. PhD students must additionally complete a qualifying examination, a research qualifier, a thesis proposal, and a thesis defense. See the Robotics Graduate Catalog for more details on degree requirements and key milestones.

 

Robotics Core (Breadth) Four courses, one from each focus area’s core course list 12.0
Robotics Electives (Depth) Four courses from the electives course list 12.0
Technical Electives Four courses in any participating robotics department (CSCI, EENG, MEGN) 12.0
MEGN/CSCI/EENG 707 GRADUATE THESIS / DISSERTATION RESEARCH CREDIT 36.0
Total Semester Hrs 72.0

Robotics Curriculum

The core Robotics program allows students to study across four key focus areas:

Perception – sensing, estimating, computer vision, mapping and localization.
Action – kinematics, dynamics, and control.
Cognition – artificial intelligence, planning and machine learning.
Interaction and Society – human-robot interaction and robot ethics.

Perception

Core Courses (Breadth)

CSCI507 INTRODUCTION TO COMPUTER VISION 3.0
CSCI573 HUMAN-CENTERED ROBOTICS 3.0
EENG519 ESTIMATION THEORY AND KALMAN FILTERING 3.0

CSCI507 INTRODUCTION TO COMPUTER VISION Equivalent with CSCI437, CSCI512, EENG507, EENG512 (I) Computer vision is the process of using computers to acquire images, transform images, and extract symbolic descriptions from images. This course provides an introduction to this field, covering topics in image formation, feature extraction, location estimation, and object recognition. Design ability and hands-on projects will be emphasized, using popular software tools. The course will be of interest both to those who want to learn more about the subject and to those who just want to use computer imaging techniques. Prerequisites: Undergraduate level knowledge of linear algebra, statistics, and a programming language. 3 hours lecture; 3 semester hours.

CSCI573 HUMAN-CENTERED ROBOTICS Equivalent with CSCI473 (II)
Human-centered robotics is an interdisciplinary area that bridges research and application of methodology from robotics, machine vision, machine learning, human-computer interaction, human factors, and cognitive science. Students will learn about fundamental research in human-centered robotics, as well as develop computational models for robotic perception, internal representation, robotic learning, human-robot interaction, and robot cognition for decision making. Students in CSCI 473 will be able to model and analyze human behaviors geared toward human-robot interaction applications. They will also be able to implement a working system using algorithms learnt to solve a given problem in human-centered robotics application. Students in CSCI 573 will get a more in-depth study into the theory of the algorithms. They will be able to compare the different algorithms to select the most appropriate one that can solve a specific problem. Prerequisites: CSCI262 and MATH201. 3 hours lecture; 3 semester hours.

EENG519 ESTIMATION THEORY AND KALMAN FILTERING (II)
Estimation theory considers the extraction of useful information from raw sensor measurements in the presence of signal uncertainty. Common applications include navigation, localization and mapping, but applications can be found in all fields where measurements are used. Mathematic descriptions of random signals and the response of linear systems are presented. The discrete-time Kalman Filter is introduced, and conditions for optimality are described. Implementation issues, performance prediction, and filter divergence are discussed. Adaptive estimation and nonlinear estimation are also covered. Contemporary applications will be utilized throughout the course. Offered in odd numbered years. Prerequisites: EENG515. 1.5 hours lecture; 1.5 hours other; 3 semester hours.

Elective Courses (Depth)

CSCI508 ADVANCED TOPICS IN PERCEPTION AND COMPUTER VISION 3.0

CSCI508 ADVANCED TOPICS IN PERCEPTION AND COMPUTER VISION Equivalent with EENG508 (II)
This course covers advanced topics in perception and computer vision, emphasizing research advances in the field. The course focuses on structure and motion estimation, general object detection and recognition, and tracking. Projects will be emphasized, using popular software tools. Prerequisites: EENG507 or CSCI507. 3 hours lecture; 3 semester hours.

Cognition

Core Courses (Breadth)

CSCI404 ARTIFICIAL INTELLIGENCE 3.0
CSCI575 MACHINE LEARNING 3.0
CSCI534 ROBOT PLANNING AND MANIPULATION 3.0

CSCI404. ARTIFICIAL INTELLIGENCE. 3.0 Semester Hrs. (II)
General investigation of the Artificial Intelligence field. Several methods used in artificial intelligence such as search strategies, knowledge representation, logic and probabilistic reasoning are developed and applied to practical problems. Fundamental artificial intelligence techniques are presented, including neural networks, genetic algorithms, and fuzzy sets. Selected application areas, such as robotics, natural language processing and games, are discussed. Prerequisite: CSCI262 with a grade of C- or higher and MATH201. 3 hours lecture; 3 semester hours.

CSCI575. MACHINE LEARNING. 3.0 Semester Hrs. (I)
The goal of machine learning research is to build computer systems that learn from experience and that adapt to their environments. Machine learning systems do not have to be programmed by humans to solve a problem; instead, they essentially program themselves based on examples of how they should behave, or based on trial and error experience trying to solve the problem. This course will focus on the methods that have proven valuable and successful in practical applications. The course will also contrast the various methods, with the aim of explaining the situations in which each is most appropriate. Prerequisite: CSCI262, MATH201, MATH332.

CSCI534. ROBOT PLANNING AND MANIPULATION. 3.0 Semester Hrs.
An introduction to planning in the context of robotics covering symbolic and motion planning approaches. Symbolic computation, symbolic domains, and efficient algorithms for symbolic planning; Robot kinematics, configuration spaces, and algorithms for motion planning. Applications of planning will focus on manipulation problems using robot arms. Prerequisite: CSCI404 or graduate student standing.

 Elective Courses – None

Action

Core Courses (Breadth)

MEGN540 MECHATRONICS 3.0
MEGN544 ROBOT MECHANICS: KINEMATICS, DYNAMICS, AND CONTROL 3.0
MEGN545 ADVANCED ROBOT CONTROL 3.0
EENG517 THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS 3.0

MEGN540. MECHATRONICS. 3.0 Semester Hrs. (II)
A course focusing on implementation aspects of mechatronic and control systems. Significant lab component involving embedded C programming on a mechatronics teaching platform, called a “haptic paddle”, a single degree-of-freedom force-feedback joystick. Prerequisite: Graduate standing. 3 hours lecture; 3 semester hours.

MEGN544. ROBOT MECHANICS: KINEMATICS, DYNAMICS, AND CONTROL. 3.0 Semester Hrs. (I)
Mathematical representation of robot structures. Mechanical analysis including kinematics, dynamics, and design of robot manipulators. Representations for trajectories and path planning for robots. Fundamentals of robot control including, linear, nonlinear and force control methods. Introduction to off-line programming techniques and simulation. Prerequisite: EENG307 and MEGN441. 3 hours lecture; 3 semester hours.

MEGN545. ADVANCED ROBOT CONTROL. 3.0 Semester Hrs.
The focus is on mobile robotic vehicles. Topics covered are: navigation, mining applications, and sensors including vision, problems of sensing variations in rock properties, problems of representing human knowledge in control systems, machine condition diagnostics, kinematics, and path planning real time obstacle avoidance. Prerequisite: EENG307.

EENG517. THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS. 3.0 Semester Hrs. Equivalent with EGGN517, (II)
This course will introduce and study the theory and design of multivariable and nonlinear control systems. Students will learn to design multivariable controllers that are both optimal and robust, using tools such as state space and transfer matrix models, nonlinear analysis, optimal estimator and controller design, and multi-loop controller synthesis. Spring semester of even years. Prerequisites: EENG417. 3 hours lecture; 3 semester hours.

 

Elective Courses (Depth)

EENG417 MODERN CONTROL DESIGN 3.0
EENG515 MATHEMATICAL METHODS FOR SIGNALS AND SYSTEMS 3.0

EENG417. MODERN CONTROL DESIGN. 3.0 Semester Hrs. (I)
Control system design with an emphasis on observer-based methods, from initial open-loop experiments to final implementation. The course begins with an overview of feedback control design technique from the frequency domain perspective, including sensitivity and fundamental limitations. State space realization theory is introduced, and system identification methods for parameter estimation are introduced. Computer based methods for control system design are presented. Prerequisite: EENG307. 3 lecture hours, 3 semester hours.

EENG515. MATHEMATICAL METHODS FOR SIGNALS AND SYSTEMS. 3.0 Semester Hrs. (I)
An introduction to mathematical methods for modern signal processing using vector space methods. Topics include signal representation in Hilbert and Banach spaces; linear operators and the geometry of linear equations; LU, Cholesky, QR, Eigen – and singular value decompositions. Applications to signal processing and linear systems are included throughout, such as Fourier analysis, wavelets, adaptive filtering, signal detection, and feedback control.

Interaction & Society

Core Courses (Breadth)

CSCI536 HUMAN-ROBOT INTERACTION 3.0
CSCI532 ROBOT ETHICS 3.0

CSCI536. HUMAN-ROBOT INTERACTION. 3.0 SEMESTER HRS.
Human-Robot Interaction is an interdisciplinary field at the intersection of Computer Science, Robotics, Psychology, and Human Factors, that seeks to answer a broad set of questions about robots designed to interact with humans (e.g., assistive robots, educational robots, and service robots), such as: (1) How does human interaction with robots differ from interaction with other people? (2) How does the appearance and behavior of a robot change how humans perceive, trust, and interact with that robot? And (3) How can we design and program robots that are natural, trustworthy, and effective? Accordingly, In this course, students will learn (1) how to design interactive robots, (2) the algorithmic foundations of interactive robots; and (3) how to evaluate interactive robots. To achieve these learning objectives, students will read and present key papers from the HRI literature, complete an individual final project tailored to their unique interests and skillsets, and complete a group project in which they will design, pilot, and evaluate novel HRI experiments, with in-class time expected to be split between lecture by the instructor, presentations by students, and either collaborative active learning activities or discussions with researchers in the field. Prerequisite: Data Structures, Probability and Statistics or equivalent.

CSCI532. ROBOT ETHICS. 3.0 Semester Hrs. (II)
This course explores ethical issues arising in robotics and human-robot interaction through philosophical analysis, scientific experimentation, and algorithm design. Topics include case studies in lethal autonomous weapon systems, autonomous cars, and social robots, as well as higher-level concerns including economics, law, policy, and discrimination. Graduate enrollees will additionally participate in and report on the results of empirical and computational robot ethics research, with the goal of developing publishable works. Prerequisite: Graduate student standing.

Elective Courses (Depth)

CSCI598 LINGUISTIC HUMAN-ROBOT INTERACTION 3.0

 CSCI598. LINGUISTIC HUMAN-ROBOT INTERACTION. 3.0 Semester Hrs. (I, II, S)
Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once, but no more than twice for the same course content. Prerequisite: none. Variable credit: 0 to 6 credit hours. Repeatable for credit under different titles.

Additional Robotics Electives

CSCI406 ALGORITHMS 3.0
CSCI561 THEORY OF COMPUTATION 3.0
CSCI562 APPLIED ALGORITHMS AND DATA STRUCTURES 3.0
CSCI565 DISTRIBUTED COMPUTING SYSTEMS 3.0
CSCI572 COMPUTER NETWORKS II 3.0
EENG411 DIGITAL SIGNAL PROCESSING 3.0
EENG511 CONVEX OPTIMIZATION AND ITS ENGINEERING APPLICATIONS 3.0
EENG521 NUMERICAL OPTIMIZATION 3.0
MEGN586 LINEAR OPTIMIZATION 3.0
MEGN587 NONLINEAR OPTIMIZATION 3.0
MEGN588 INTEGER OPTIMIZATION 3.0
MEGN686 ADVANCED LINEAR OPTIMIZATION 3.0
MEGN688 ADVANCED INTEGER OPTIMIZATION 3.0

CSCI406. ALGORITHMS. 3.0 Semester Hrs. Equivalent with MATH406, (I, II)
Reasoning about algorithm correctness (proofs, counterexamples). Analysis of algorithms: asymptotic and practical complexity. Review of dictionary data structures (including balanced search trees). Priority queues. Advanced sorting algorithms (heapsort, radix sort). Advanced algorithmic concepts illustrated through sorting (randomized algorithms, lower bounds, divide and conquer). Dynamic programming. Backtracking. Algorithms on unweighted graphs (traversals) and weighted graphs (minimum spanning trees, shortest paths, network flows and bipartite matching); NP-completeness and its consequences. Prerequisite: CSCI262 with a grade of C- or higher, (MATH213 or MATH223 or MATH224), and (MATH300 or MATH358 or CSCI358). 3 hours lecture; 3 semester hours.

CSCI561. THEORY OF COMPUTATION. 3.0 Semester Hrs. (I)
An introduction to abstract models of computation and computability theory; including finite automata (finite state machines), pushdown automata, and Turing machines. Language models, including formal languages, regular expressions, and grammars. Decidability and undecidability of computational problems. 3 hours lecture; 3 semester hours. Prerequisite: CSCI406.

CSCI562. APPLIED ALGORITHMS AND DATA STRUCTURES. 3.0 Semester Hrs. (II)
Industry competitiveness in certain areas is often based on the use of better algorithms and data structures. The objective of this class is to survey some interesting application areas and to understand the core algorithms and data structures that support these applications. Application areas could change with each offering of the class, but would include some of the following: VLSI design automation, computational biology, mobile computing, computer security, data compression, web search engines, and geographical information systems. Prerequisite: MATH/CSCI406. 3 hours lecture; 3 semester hours.

CSCI565. DISTRIBUTED COMPUTING SYSTEMS. 3.0 Semester Hrs. (II)
This course discusses concepts, techniques, and issues in developing distributed systems in large scale networked environment. Topics include theory and systems level issues in the design and implementation of distributed systems. Prerequisites: CSCI 442 or equivalent. 3 hours of lecture; 3 semester hours.

CSCI572. COMPUTER NETWORKS II. 3.0 Semester Hrs.
This course explores how computer networking is evolving to support new environments, and challenges in building networked systems that are simultaneously highly robust, efficient, flexible, and secure. Detailed topics include wireless and mobile networks, multimedia networking, and network security. In addition, recent research and developments are also studied, which include mobile sensing, Internet of Things (IoT), social computing and networks, mobile ad-hoc networks, wireless sensor networks, software defined networking, and future Internet architecture. Prerequisite: CSCI262 or equivalent or instructor consent.

EENG411. DIGITAL SIGNAL PROCESSING. 3.0 Semester Hrs. (II)
This course introduces the mathematical and engineering aspects of digital signal processing (DSP). An emphasis is placed on the various possible representations for discrete-time signals and systems (in the time, z-, and frequency domains) and how those representations can facilitate the identification of signal properties, the design of digital filters, and the sampling of continuous-time signals. Advanced topics include sigma-delta conversion techniques, multi-rate signal processing, and spectral analysis. The course will be useful to all students who are concerned with information bearing signals and signal processing in a wide variety of application settings, including sensing, instrumentation, control, communications, signal interpretation and diagnostics, and imaging. Prerequisite: EENG310. 3 hours lecture; 3 semester hours.

EENG511. CONVEX OPTIMIZATION AND ITS ENGINEERING APPLICATIONS. 3.0 Semester Hrs.
The course focuses on recognizing and solving convex optimization problems that arise in applications in various engineering fields. Covered topics include basic convex analysis, conic programming, duality theory, unconstrained optimization, and constrained optimization. The application part covers problems in signal processing, power and energy, machine learning, control and mechanical engineering, and other fields, with an emphasis on modeling and solving these problems using the CVX package. Offered spring semester of even years. Prerequisites: EENG311, EENG515.

EENG521. NUMERICAL OPTIMIZATION. 3.0 Semester Hrs.
Optimization is an indispensable tool for many fields of science and engineering. This course focuses on the algorithmic aspects of optimization. Covered topics include first-order (gradient descent and its variants) and second-order methods (Newton and quasi-Newton methods) for unconstrained optimization, theory and algorithms for constrained optimization, stochastic optimization and random search, derivative-free optimization, dynamic programming and simulation-based optimization, and distributed and parallel optimization. The emphasis will be on how the algorithms work, why they work, how to implement them numerically, and when to use which algorithm, as well as applications in different science and engineering fields. Prerequisite: EENG515 or instructor consent.

MEGN586. LINEAR OPTIMIZATION. 3.0 Semester Hrs. (I)
We address the formulation of linear programming models, linear programs in two dimensions, standard form, the Simplex method, duality theory, complementary slackness conditions, sensitivity analysis, and multi-objective programming. Applications of linear programming models include, but are not limited to, the areas of manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Offered every other year. 3 hours lecture; 3 semester hours.

MEGN587. NONLINEAR OPTIMIZATION. 3.0 Semester Hrs. (II) Equivalent with MEGN487
We address both unconstrained and constrained nonlinear model formulation and corresponding algorithms (e.g., Gradient Search and Newton’s Method, and Lagrange Multiplier Methods and Reduced Gradient Algorithms, respectively). Applications of state-of-the-art hardware and software will emphasize solving real-world engineering problems in areas such as manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with an algorithm such as MINOS) these optimization problems is introduced. Prerequisite: MATH111. 3 hours lecture; 3 semester hours.

MEGN588. INTEGER OPTIMIZATION. 3.0 Semester Hrs. (I) Equivalent with MEGN488
We address the formulation of integer programming models, the brand-and-bound algorithm, total unimodularity and the ease with which these models are solved, and then suggest methods to increase tractability, including cuts, strong formulations, and decomposition techniques, e.g., Lagrangian relaxation, Benders decomposition. Applications include manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Prerequisite: none. 3 hours lecture; 3 semester hours. Years to be offered: Every Other Year.

MEGN686. ADVANCED LINEAR OPTIMIZATION. 3.0 Semester Hrs. (II)
As an advanced course in optimization, we expand upon topics in linear programming: advanced formulation, the dual simplex method, the interior point method, algorithmic tuning for linear programs (including numerical stability considerations), column generation, and Dantzig-Wolfe decomposition. Time permitting, dynamic programming is introduced. Applications of state-of-the-art hardware and software emphasize solving real-world problems in areas such as manufacturing, mining, energy, transportation and logistics, and the military. Computers are used for model formulation and solution. Offered every other year. Prerequisite: MEGN586. 3 hours lecture; 3 semester hours.

MEGN688. ADVANCED INTEGER OPTIMIZATION. 3.0 Semester Hrs. (II)
As an advanced course in optimization, we expand upon topics in integer programming: advanced formulation, strong integer programming formulations (e.g., symmetry elimination, variable elimination, and persistence), in-depth mixed integer programming cuts, rounding heuristics, constraint programming, and decompositions. Applications of state-of-the-art hardware and software emphasize solving real-world problems in areas such as manufacturing, mining, energy, transportation and logistics, and the military. Computers are used for model formulation and solution. Prerequisite: MEGN588. 3 hours lecture; 3 semester hours. Years to be offered: Every Other Year.