Program of Study

The main emphasis of the Ph.D. program is the successful completion of an original and independent research thesis. The degree requirements are designed around this goal.

Minimum Requirements

  • Completion of 36 semester hours of courses with a letter grade
  • Passing a comprehensive qualifying exam with written and oral components.
  • Successfully conducting, documenting, and defending a piece of original research culminating in a doctoral thesis.

Ph.D. Robotics Degree Requirements – 36 semester hours with a letter grade

Component Courses Hours Required
Intro to Robotics Research A new course CS/AE/ECE/ME 7785, Introduction to Robotics Research.  3
Foundation Courses Three foundation courses, each selected from distinct core areas: Mechanics, Controls, Perception, Artificial Intelligence, and Human-Robot Interaction (HRI). 9
Elective Courses Three targeted elective courses, each selected from the same three core areas used for the foundation courses.  9
Multidisciplinary Robotics Research Two new courses CS/AE/ECE/ME 8750 and CS/AE/ECE/ME 8751, Multidisciplinary Robotics Research I and II.  6
Courses Outside the Major Three courses outside the major area to provide a coherent minor in accordance with Institute policies.  9
  TOTAL 36

*A maximum of two classes (6 semester hours) at the 4000 level may be used to satisfy the 36 semester hour requirement.

Ph.D. Candidacy

Prior to completing all of these requirements, Georgia Tech defines the Ph.D Candidate milestones. Admission to candidacy requires that the student:

  1. Complete all course requirements (except the minor);
  2. Achieve a satisfactory scholastic record;
  3. Pass the comprehensive examination;
  4. Submit and receive approval naming the dissertation topic and delineating the research topic.

(Georgia Institute of Technology 2006-2007 General Catalog, p. 122)

Core Area Courses

The following courses are in the robotics core areas of Mechanics, Control, Perception, Artificial Intelligence, and Human-Robot Interaction (HRI). They are used to select three foundation courses and three targeted elective courses.

Foundation courses are marked by an asterisk (*).

Component Courses
Mechanics
  • AE 6210*, Advanced Dynamics I – Kinematics of particles and rigid bodies, angular velocity, inertia properties, holonomic and nonholonomic constraints, generalized forces. Prerequisite: AE 2220. 3 credit hours
  • AE 6211, Advanced Dynamics II – A continuation of AE 6210. Equations of motion, Newtonian frames, consistent linearization, energy and momentum integrals, collisions, mathematical representation of finite rotation. Prerequisite: AE 6210. 3 credit hours
  • AE 6230, Structural Dynamics – Dynamic response of single-degree-of-freedom systems, Lagrange's equations; modal decoupling; vibration of Euler-Bernoulli and Timoshenko beams, membranes and plates. Prerequisites: AE 3120, AE 3515. 3 credit hours
  • AE 6263, Flexible Multi-Body Dynamics – Nonlinear, flexible multi-body dynamic systems, parameterization of finite rotations, strategies for enforcement of holonomic and non holonomic constraints, formulation of geometrically nonlinear structural elements, time-integration techniques. Prerequisites: AE 6211, AE 6230. 3 credit hours
  • AE 6270, Nonlinear Dynamics – Nonlinear vibration methods through averaging and multiple scales, bifurcation, periodic and quasi-periodic systems, transition to chaos, characterization of chaotic vibrations, thermodynamics of chaos, chaos control. Prerequisite: AE 6230. 3 credit hours
  • AE 6520, Advanced Flight Dynamics — Reference frames and transformations, general equations of unsteady motion, application to fixed-wing, rotary-wing and space vehicles, stability characteristics, flight in turbulent atmosphere. 3 credit hours
  • BMED 8813*, Robotics — Robot kinematics, statics, and dynamics. Open-chain manipulators and parallel manipulators as well as an understanding of trajectory planning and non-holonomic systems. 3 credit hours
  • CS 7496, Computer Animation — Motion techniques for computer animation and interactive games (keyframing, procedural methods, motion capture, and simulation) and principles for storytelling, composition, lighting, and interactivity. 3 credit hours
  • ME 6405, Introduction to Mechatronics – Modeling and control of actuators and electro-mechanical systems. Performance and application of microprocessors and analog electronics to modern mechatronic systems. Prerequisites ME 3015 or equivalent, or with the consent of the instructor. 3 credit hours
  • ME 6407*, Robotics – Analysis and design of robotic systems including arms and vehicles. Kinematics and dynamics. Algorithms for describing, planning, commanding and controlling motion force. Prerequisites ME 3015 or ECE 3085. 3 credit hours
  • ME 6441*, Dynamics of Mechanical Systems – Motion analysis and dynamics modeling of systems of particles and rigid bodies in three-dimensional motion. Prerequisites: ME 3015 or equivalent, or with the consent of the instructor. 3 credit hours
  • ME 6442, Vibration of Mechanical Systems – Introduction to modeling and oscillatory response analysis for discrete and continuous mechanical and structural systems. Prerequisites: ME 3015 and ME 3201. 3 credit hours
  • ME 7442, Vibration of Continuous Systems – Equations of motion and oscillatory response of dynamic systems modeled as continuous media. Prerequisites: ME 6442 or equivalent, or with the consent of the instructor. 3 credit hours
Control
  • AE 6252, Smart Structure Control – Modeling smart sensors and actuators, development of closed loop models, design of controllers, validation of controllers, application to vibration control, noise control, and shape control. Prerequisite: AE 6230. 3 credit hours
  • AE 6504, Modern Methods of Flight Control – Linear quadratic regulator design. Model following control. Stochastic control. Fixed structure controller design. Applications to aircraft flight control. Prerequisite: AE 3521. 3 credit hours
  • AE 6505, Kalman Filtering – Probability and random variables and processes; correlation; shaping filters; simulation of sensor errors; Wiener filter; random vectors; covariance propagation; recursive least-squares; Kalman filter; extensions. Prerequisite: AE 3515. 3 credit hours
  • AE 6506, Guidance and Navigation – Earth's shape and gravity. Introduction to inertial navigation. GPS aiding. Error analysis. Guidance systems. Analysis of the guidance loop. Estimation of guidance variables. Adjoint analysis. Prerequisite: AE 3521. 3 credit hours
  • AE 6511, Optimal Guidance and Control – Euler-Lagrange formulation; Hamilton-Jacobi approach; Pontryagin's minimum principle; Systems with quadratic performance index; Second variation and neighboring extremals; Singular solutions; numerical solution techniques. Prerequisite: AE 3515. 3 credit hours
  • AE 6531, Robust Control I – Robustness issues in controller analysis and design. LQ analysis, H2 norm, LQR, LQG, uncertainty modeling, small gain theorem, H-infinity performance, and the mixed-norm H2/H-infinity problem. Prerequisite: ECE 6550. 3 credit hours
  • AE 6532, Robust Control II – Advanced treatment of robustness issues. Controller analysis and design for linear and nonlinear systems with structured and non-structured uncertainty. Reduced-order control, stability, multipliers, and mixed-mu. Prerequisite: ECE 6531. 3 credit hours
  • AE 6534, Control of AE Structures – Advanced treatment of control of flexible structures. Topics include stability of multi-degree-of-freedom systems, passive and active absorbers and isolation, positive real models, and robust control for flexible structures. Prerequisite: ECE 6230, ECE 6531. 3 credit hours
  • AE 6580, Nonlinear Control – Advanced treatment of nonlinear robust control. Lyapunov stability theory, absolute stability, dissipativity, feedback linearization, Hamilton-Jacobi-Bellman theory, nonlinear H-infinity, backstepping control, and control Lyapunov functions. Prerequisite: ECE 6550. 3 credit hours
  • AE 8803 THE, Nonlinear Stochastic Optimal Control 3 credit hours
  • ECE 6550*, Linear Systems and Controls – Introduction to linear system theory and feedback control. Topics include state space representations, controllability and observability, linear feedback control. Prerequisite: Graduate Standing. 3 credit hours
  • ECE 6551, Digital Controls – Techniques for analysis and synthesis of computer-based control systems. Design projects provide an understanding of the application of digital control to physical systems. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ECE 6552, Nonlinear Systems and Control – Classical analysis techniques and stability theory for nonlinear systems. Control design for nonlinear systems, including robotic systems. Includes design projects. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ECE 6553, Optimal Control and Optimization – Optimal control of dynamic systems, numerical optimization, techniques and their applications in solving optical-trajectory problems. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ECE 6554, Adaptive Control – Methods of parameter estimation and adaptive control for systems with constant or slowly varying unknown parameters. Includes MATLAB design projects emphasizing applications to physical systems. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ECE 6555, Optimal Estimation – Techniques for signal and state estimation in the presence of measurement and process noise with the emphasis on Wiener and Kalman filtering. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ECE 6559, Advanced Linear Systems – Study of multivariable linear system theory and robust control design methodologies. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ME 6401*, Linear Control Systems – Theory and applications of linear systems, state space, stability, feedback controls, observers, LQR, LQG, Kalman Filters. Prerequisite: ME 3015 or equivalent, or with the consent of the instructor. 3 credit hours
  • ME 6402, Nonlinear Control Systems – Analysis of nonlinear systems, geometric control, variable structure control, adaptive control, optimal control, applications. Prerequisite: ME 6401 or equivalent, or with the consent of the instructor. 3 credit hours
  • ME 6403, Digital Control Systems – Comprehensive treatment of the representation, analysis, and design of discrete-time systems. Techniques include Z- and W- transforms, direct method, control design, and digital tracking. Prerequisite: ME 3015 or equivalent, or with the consent of the instructor. 3 credit hours
  • ME 6404, Advanced Control System Design and Implementation – Analysis, synthesis and implementation techniques of continuous-time and real-time control systems using classical and state-space methods. Prerequisite: ME 6403 or equivalent, or with the consent of the instructor. 3 credit hours
Perception
  • CS 6476*, Computer Vision – Introduction to computer vision including fundamentals of image formation, camera imaging geometry, feature detection and matching, stereo, motion estimation and tracking, image classification and scene understanding. Credit not awarded for both CS 6476 and CS 4495 or CS 4476. 3 credit hours
  • CS 7476, Advanced Computer Vision – Advanced topics in computer vision, which includes a deep dive into both the theoretical foundations of computer vision to the practical issues of building real systems that use computer vision. Credit not awarded for CS 7476 and CS 7495. 3 credit hours
  • CS 7616, Pattern Recognition – This course provides an introduction to the theory and practice of pattern recognition.It emphasizes unifying concepts and the analysis of real-world datasets. 3 credit hours
  • CS 7636, Computational Perception – Study of statistical and algorithmic methods for sensing people using video and audio. Topics include face detection and recognition, figure tracking, and audio-visual sensing. Prerequisites: CS 4641 and (CS 4495 or CS 7495) 3 credit hours
  • CS 8803, 3D Reconstruction and Mapping – Course focuses on multi-robot/multi-camera mapping and reconstruction. Topics range from SLAM, graphical model inferences, and understanding the practical issues regarding multi-platform reconstruction. 3 credit hours
  • CS 8803, BHI Behavioral Imaging – Theory and methods for measuring, recognizing, and quantifying social and communicative behavior using video, audio, and wearable sensor data. 3 credit hours
  • CS 8803 DL, Deep Learning for Perception 3 credit hours
  • ECE 6255, Digital Processing of Speech Signals – The application of digital signal processing to problems in speech communication. Includes a laboratory project. Prerequisites: ECE 4270 Minimum Grade of D. 3 credit hours
  • ECE 6258, Digital Image Processing – An introduction to the theory of multidimensional signal processing and digital image processing, including key applications in multimedia products and services, and telecommunications. Prerequisites: ECE 4270 Minimum Grade of D. 3 credit hours
  • ECE 6273, Pattern Recognition – Theory and application of pattern recognition with a special application section for automatic speech recognition and related signal processing. Prerequisites: ECE 4270 Minimum Grade of D. 3 credit hours
  • ECE 6560, PDEs in Image Processing and Computer Vision – Mathematical foundations and numerical aspects of partial-differential equation techniques used in computer vision. Topics include image smoothing and enhancement, edge detection, morphology, and image reconstruction. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
  • ME 6406, Machine Vision – Design of algorithms for vision systems for manufacturing, farming, construction, and the service industries. Image processing, optics, illumination, feature representation. Prerequisite: Graduate Standing in engineering or related discipline. 3 credit hours
Artificial Intelligence
  • CS 3600, Introduction to Artificial Intelligence – An introduction to artificial intelligence and machine learning. Topics include intelligent system design methodologies, search and problem solving, supervised and reinforced learning. Prerequisites: CS 1332
  • CS 6601*, Artificial Intelligence – Basic concepts and methods of artificial intelligence including both symbolic/conceptual and numerical/probabilistic techniques. Prerequisites: CS 2600
  • CS 7612, AI Planning – Symbolic numerical techniques that allow intelligent systems to decide how they should act in order to achieve their goals, including action and plan representation, plan synthesis and reasoning, analysis of planning algorithms, plan execution and monitoring, plan reuse and learning, and applications. Prerequisites: CS 6601
  • CS 7640, Learning in Autonomous Agents – An in-depth look at agents that learn, including intelligent systems, robots, and humans. Design and implementation of computer models of learning and adaptation in autonomous intelligent agents. Prerequisites: CS 3600 or CS 4641
  • CS 7641 Machine Learning – Machine learning techniques and applications. Topics include foundational issues; inductive, analytical, numerical, and theoretical approaches; and real-world applications. Prerequisites: CS 6601
  • CS 8803, Mobile Manipulation – The objective of the course is to gain knowledge of methods for design of mobile manipulation systems. The course covers all aspects of the problem from navigation and localization over kinematics and control to visual and force based perception.
  • CS 8803, Robot Intelligence: Planning in Action – Course covers methods for planning with symbolic, numerical, geometric and physical constraints. Topics will range from classical and stochastic planning to continuous robot domains and hybrid control of dynamic systems.
  • CS 8803, Computation and the Brain
  • CS 8803, Special Topics on Reinforcement Learning
  • CS 8803, Statistical Techniques in Robotics
  • ECE 6556, Intelligent Control – Principles of intelligent systems and their utility in modeling, identification, and control of complex systems; neuro-fuzzy tools applied to supervisory control; hands-on laboratory experience. Prerequisites: ECE 6550 Minimum Grade of D. 3 credit hours
Autonomy Discontinued—No longer offered beginning in Fall 2016. 
Human-Robot Interaction (HRI)

HRI includes two core courses. Students are encouraged, but not required to take both HRI core courses. Students taking both core courses may use their second core class in place of an HRI elective course.

  • AE 6721*, Evaluation of Human Integrated Systems – Evaluation of human integrated systems including translating research questions into measurable objectives, overview of evaluation methods and data analysis techniques applicable to such systems. 3 credit hours
  • CS 7633*, Human-Robot Interaction – Survey of the state of the art in HRI research, introduction to statistical methods for HRI research, research project studio. A petition has been filed for this to be added to the permanent CS curriculum and have permanent course number. 3 credit hours
  • This course will become ineligible as an AI elective beginning in Spring Semeter 2017—APPH 6203, Biomechanics/Kinesiology in Prosthetics and Orthotics – Specific to prosthetics and orthotics information related to the use of skeletal muscle as a resource to the nervous system are presented. Muscle synergies, limb-based dynamics, total body mechanics and local and central neural control systems and logic are discussed. 2 credit hours
  • CS 6455, User Interface Design and Evaluation – Qualitative empirical methods for understanding human-technology interaction. 3 credit hours
  • CS 6750, Human-Computer Interact – Describes the characteristics of interaction between humans and computers and demonstrates techniques for the evaluation of user-centered systems. 3 credit hours
  • CS 8803 CSR, Computational Social Robotics 3 credit hours
  • ISYE 6215, Human-Machine Systems – The development and use of mathematical models of human behavior are considered. Approaches from estimation theory, control theory, queuing theory, and fuzzy set theory are considered. 3 credit hours
  • ISYE 6224, Human-Integrated Systems – State-of-the-art research directions including supervisory control models of human command control tasks; human-computer interface in scheduling and supervision of flexible manufacturing systems. 3 credit hours
  • PSYC 6011, Cognitive Psychology – Survey course on human cognition including pattern recognition, attention, memory, categorization, problem solving, consciousness, decision making, intention, and the relation between mind and brain.
  • PSYC 6014, Sensation & Perception – This course examines how sensations and perceptions of the outside world are processed by humans, including physiological, psychophysical, ecological, and computational perspectives. 3 credit hours
  • PSYC 6017, Human Abilities – Theory, methods, and applications of research on human abilities, including intelligence, aptitude, achievement, learning, aptitude treatment interactions, information processing correlates, and measurement issues. 3 credit hours
  • PSYC 7101, Engineering Psych I – Basic methods used to study human-machine systems including both system analysis and human performance evaluation techniques. These methods will be applied to specific systems. 3 credit hours
  • PSYC 7104, Psychomotor & Cog Skill – Human capabilities and limitations for learning and performing psychomotor and cognitive skills are studied. 3 credit hours
* indicates foundation course

Required Fundamental Courses

Three required fundamental courses are designed specifically for the Robotics Ph.D.:

Course Details
CS/AE/ECE/ME 7785
Introduction to Robotics Research

Provides students with a familiarization of the core areas of robotics including Mechanics, Control, Perception, Artificial Intelligence, and Autonomy. Provides an introduction to the fundamental mathematical tools required in robotics research. (3 credit hours).

The desired learning outcome is to provide a strong theoretical foundation for students on the multidisciplinary subject matters found in robotics. This is accomplished by:

  1. Providing an introduction to the fundamentals of robotics in the core areas of mechanics, control, perception, artificial intelligence, and autonomy.
  2. Providing the basic theoretical and mathematical tools to support the core areas in robotics.
  3. The evaluation component includes:
  • Mid-term and final exams to evaluate student understanding of course material.
  • Written homework assignments to reinforce and apply lecture materials.
  • Group project and presentation to apply theoretical understanding to real-world applications.

CS/AE/ECE/ME 8750
Multidisciplinary Robotics Research I
(3 credit hours)
Prerequisite: CS/AE/ECE/ME 7785

CS/AE/ECE/ME 8751
Multidisciplinary Robotics Research II
(3 credit hours)
Prerequisite: CS/AE/ECE/ME 8750

These courses form a two semester sequence with similar “laboratory-rotation” formats. Each course requires the student to complete a semester-long research project under the guidance of at least two faculty members from distinct participating schools (AE, BME, CoC, ECE, or ME). The courses are designed to expose students to the discipline of research in a structured way and to encourage novel ideas in a multidisciplinary context.

The desired learning outcome is to foster a multidisciplinary research approach in the student by:

  • Critically assessing the prior art in an area outside his/her own,
  • Performing state-of-the-art experimental or simulation work in a multidisciplinary area,
  • Coherently reporting, at the level of a conference publication, on the research performed.

The evaluation component includes:

  • Week 2, a one page proposal outlining the proposed work along with a well-argued motivation;
  • Week 5: a detailed written review paper of the state-of-the art in the area;
  • Week 10: a written report on the experimental or simulation component in progress;
  • Week 14: a final report and presentation that includes all of the above along with a discussion of the work done and opportunities for future work.

All deliverables will be graded by both faculty advisors as well as reviewed to comply with the evaluation criteria set by the Robotics Program Committee.

Qualifying Exam

The purpose of the comprehensive exam is to:

  • Assess the student's general knowledge of the degree area
  • Assess the student's specialized knowledge of the chosen research area

The comprehensive examination provides an early assessment of the student's potential to satisfactorily complete the requirements for the doctoral degree. As such, it requires that fundamental principles be mastered and integrated so that they can be applied to solving problems relevant to robotics.

Procedure

After three regular semesters (fall or spring) from entering the Ph.D. program, the student must take the comprehensive examination at the next scheduled offering, usually during the fourth regular (i.e.; fall or spring) semester. If the comprehensive examination is failed, the student may have one additional opportunity at the next scheduled offering. The examination will be offered at least once every year.

The comprehensive exam is a written and oral examination and is administered by a faculty committee consisting of Core Area Chairs and the Program Director. Students are required to declare two areas of focus from three core areas when they register for the qualifying exam. A student’s advisor is allowed to sit in on the oral exam as a silent observer.

Mandatory Quals Appeals Process

If a student fails the qualifying exam on his or her second attempt, he or she goes through a mandatory appeals process. Ultimately, this process results in a decision to either designate the student as fully qualified and in good standing, in spite of the result of the qualifying exam, or to proceed with the expulsion of the student from the Robotics Ph.D. program. For exceptional circumstances, the Robotics Ph.D. Committee may make a positive decision to designate a student as fully qualified prior to the full committee meeting. Any outcome that would result in expulsion of a student must be made at a full committee meeting with an agenda comparable to the this template.

Ph.D. Thesis

The Ph.D. dissertation describes the results of a research project and demonstrates that the candidate possesses powers of original thought, talent for research, and ability to organize and present findings.

Dissertation Advisory Committee

The student presents and defends a written Ph.D. proposal to a Dissertation Advisory Committee of at least five faculty members approved by the Robotics Program Committee. The Dissertation Advisory Committee consists of five or more members where:

  • At least three members must be faculty affiliated with the Robotics Program or from the student's Home School (CoC, AE, BME, ECE, ME).
  • At least two members must be from outside of the student’s Home School

Ph.D. Dissertation Proposal

The objective of the Ph.D. Proposal is to allow an early assessment of your chosen topic of research for the satisfactory completion of the doctoral degree. The proposal should delineate your specific area of research by stating the purpose, scope, methodology, overall organization, and limitations of the proposed study area. The proposal must include a review of the relevant literature and indicate the expected contribution of the research.

The proposal should be organized as follows:

  • Summary - limited to 200 words.
  • Table of Contents
  • Project Description - a clear statement of the work to be undertaken. Limited to 15 pages single spaced (30 pages double spaced) and including all graphic elements and tables.
  • Bibliography

Pages should be of standard size (8½" x 11"; 21.6 cm x 27.9 cm) with minimum 1" or 2.5 cm margins at the top, bottom, and on each side. The minimum type font size is 10 to 12 points.

Dissertation Defense

The dissertation, when completed, must be publicly defended before an Examination Committee approved by the Graduate Studies office. In most instances the Examination Committee is expected to be the same as the Dissertation Advisory Committee. If a candidate should fail to pass the final oral examination, the Examining Committee may recommend permission for one additional examination. It is expected that the dissertation results will be published in peer-reviewed journals and conferences.

Details on preparing and submitting a dissertation according to institute guidelines are available on the Graduate Admissions website.

Residency Requirement

“Doctoral students must spend at least two full-time semesters in residence at the Georgia Institute of Technology and ordinarily must complete research for the dissertation while in residence.” (Georgia Tech 2009-10 General Catalog)