Education - GRASP Lab @ Penn

Education

Master's of Science in Engineering (M.S.E.) in Robotics

Courses

ESE 500 Linear Systems Theory. Prerequisite(s): Open to graduates and undergraduates that have taken undergraduate courses in linear algebra and differential equations.

This graduate level course focuses on linear system theory in time domain based on linear operators. The course introduces the fundamental mathematics of linear spaces, linear operator theory, and then proceeds with existence and uniqueness of solutions of differential equations, the fundamental matrix solution and state transition matrix for time-varying linear systems. It then focuses on the fundamental concepts of stability, controllability, and observability, feedback, pole placement, observers, output feedback, kalman filtering, linear quadratic regulator. Special topics such as optimal control, robust, geometric linear control will be considered as time permits.

ESE 505 (ESE 406, MEAM513) Control of Systems.

Basic methods for analysis and design of feedback control in systems. Applications to practical systems. Methods presented include time response analysis, frequency response analysis, root locus, Nyquist and Bode plots, and the state-space approach.

CIS 510 (CSE 410) Curves and Surfaces: Theory and Applications Prerequisite(s): Basic knowledge of linear algebra, calculus, and elementary geometry. CIS 560 is not required.

The course is about mathematical and algorithmic techniques used for geometric modeling and geometric design, using curves and surfaces. There ar emany applicaiatons in computer graphics as well as in robotics, vision, and computational geometry. Such techniques are used in 2D and 3D drawing and plot, object silhouettes, animating positions, product design (cars, planes, buidlings), topographic data, medical imagery, active surfaces of proteins, attribute maps (color, texture, roughness), weathr data, art, etc. Three broad classes of problems will be considered: approximating curved shapes, using smooth curves or surfaces. Interpolating curved shapes, using smooth curves or surfaces. Rendering smoth curves or surfaces.

MEAM 510 (MEAM410) Design of Mechatronic Systems. Prerequisite(s): Junior or Senior standing in MEAM and a first course in electronics (e.g. EE 215/205 or equivalent course), or permission of the instructor. This course is a cross-listed course with an advanced level undergraduate course. It may be taken by M.S.E. students for credit. M.S.E. students will be required to do some extra work, they will be graded on a different grade scale than undergraduate students, and they will be required to demonstrate a higher level of maturity in their class assignments. MEAM doctoral candidates will not be permitted to count 400/500 courses as a part of their degree requirments.

This course is intended to provide an integrated introduction to the design of electromechanical systems. The central focus of this course will be the completion of a team-based project, to be tested in an in-class competition during the final week of the course. Topics to be covered include: a review of mechanics, basics of electromagnetics, instrumentation, sensing and measurement, actuation and actuator dynamics (electric, pneumatic, and hydraulic), analog and digital interfacing, micro-processor technology and programming, basic control theory, including linearization, stability, and real-time control, sampling and aliasing; advanced materials (piezoelectrics, electro-rheological gels, PVDF films, SMA's), and active damping. Examples and laboratory assignments will be taken from applications such as disk drives, HVAC controls, robotic manipulators, and an SMA-driven walking robot.

CIS 520 Artificial Intelligence and Machine Learning. Prerequisite(s): Elementary probability, calculus, and linear algebra. Basic programming experience.

This course will provide a survey of mathematical methods and programming techniques in artificial intelligence, pattern recognition, machine learning, and neural computation. Topics include: inference and learning in probabilistic graphical models; autonomous agents, decision-making, and reinforcement learning; neural networks and biologically inspired models of computation; statistical methods for prediction, clustering, and dimensionality reduction; and applications to vision, robotics, speech, and natural language processing.

MEAM 520 (CSE 390, MEAM420) Robotics and Automation. Prerequisite(s): Graduate standing in engineering or permission of instructor. Alternate years.

This course is for seniors and graduate students interested in robotics. It deals with the kinematics, dynamics, control and programming of robot manipulators and mobile robots. The laboratory component of the course focuses on actuators, sensors, transmissions, controllers, and applications of robotics and automation in industry.

MEAM 535 Advanced Dynamics.

This is a graduate level course dealing with the dynamics of mechanical systems. The topics include a review of Newtonian mechanics, Lagrangian and Hamiltonian mechanics, stability of dynamical systems, simulation, variational calculus, and an introduction to the dynamics of continuous systems.

CIS 580 Machine Perception. Prerequisite(s): A solid grasp of the fundamentals of linear algebra. Some knowledge of programming in C and/or Matlab.

An introduction to the problems of computer vision and other forms of machine perception that can be solved using geometrical approaches rather than statistical methods. Emphasis will be placed on both analytical and computational techniques. This course is designed to provide students with an exposure to the fundamental mathematical and algorithmic techniques that are used to tackle challenging image based modeling problems. The subject matter of this course finds application in the fields of Computer Vision, Computer Graphics and Robotics. Some of the topics to be covered include: Projective Geometry, Camera Calibration, Image Formation, Projective, Affine and Euclidean Transformations, Computational Stereopsis, and the recovery of 3D structure from multiple 2D images. This course will also explore various approaches to object recognition that make use of geometric techniques, these would include alignment based methods and techniques that exploit geometric invariants. In the assignments for this course, students will be able to apply the techniques to actual computer vision problems.

ESE 601 Hybrid Systems. Prerequisite(s): graduate students that have taken undergraduate courses on linear algebra and calculus. Also, it is assumed that the students have some working knowledge on some programming language, such as C or MATLAB. Some knowledge about linear systems theory, discrete event systems theory and probability theory is an advantage. However, the course will provide a short review on the necessary background material.

The course will be centered around the emerging field of hybrid systems. Started with introductory material, including a review on necessary background material, the course will cover a number of contemporary topics in hybrid systems. Topics such as, modeling and simulation, and verification of hybrid systems will be covered, together with an introduction to relevant software tools. We shall also discuss the use of hybrid systems in modeling real systems, such as robotics, biological systems, transportation systems, etc. Other relevant topics, such as, systems abstraction, stability analysis, controller synthesis and stochastic hybrid systems will also be covered, starting with introductory until state-of-the-art material.

ESE 605 Modern Convex Optimization. Prerequisite(s): Knowledge of linear algebra and willingness to do programming. Exposure to numerical computing, optimization, and application fields is helpful but not required.

This course concentrates on recognizing and solving convex optimization problems that arise in engineeering. Topics include: convex sets, functions, and optimization problems. Basis of convex analysis. Linear, quadratic, geometric, and semidefinite programming. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods, ellipsoid algorithm and barrier methods, self-concordance. Applications to signal processing, control, digital and analog circuit design, computation geometry, statistics, and mechanical engineering.

CIS 610 (MATH676) Advanced Geometric Methods in Computer Science. Prerequisite(s): CIS 510 or coverage of equivalent material.

The purpose of this course is to present some of the advanced geometric methods used in geometric modeling, computer graphics, computeer vision, etc. The topics may vary from year to year, and will be selected among the following subjects (nonexhaustive list): Introduction to projective geometry with applications to rational curves and surfaces, control points for rational curves, retangular and triangular rational patches, drawing closed rational curves and surfaces; Differential geometry of curves (curvature, torsion, osculating planes, the Frenet frame, osculating circles, osculating spheres); Differential geometry of surfaces (first fundamental form, normal curvature, second fundamental form, geodesic curvature, Christoffel symbols, principal curvatures, Gaussian curvature, mean curvature, the Gauss map and its derivative dN, the Dupin indicatrix, the Theorema Egregium equations of Codazzi-Mainadi, Bonnet's theorem, lines of curvatures, geodesic torsion, asymptotic lines, geodesic lines, local Gauss-Bonnet theorem).

ESE 617 (CBE 617, CIS 613, MEAM613) Non-Linear Control Theory. Prerequisite(s): Undergraduate Control course.

This courses focuses on nonlinear systems, planar dynamical systems, Poincare Bendixson Theory, index theory, bifurcations, Lyapunov stability, small-gain theorems, passivity, the Poincar map, the center manifold theorem, geomentric control theory, and feedback linearization.

CIS 620 Advanced Topics in Artificial Intelligence. Prerequisite(s): CIS 520 or equivalent.

Discussion of problems and techniques in Artificial Intelligence (AI): Knowledge Representation, Natural Language Processing, Constraint Systems, Machine Learning; Application of AI.

MEAM 620 Robotics and Motion Planing. Prerequisite(s):

This course deals with the robot kinematics and motion planning. After this class, people will be expected to use and develop algorithms to solve motion planning problems. Students are expected to have a basic background in physics and must have had basic courses in algorithms, ordinary differential equations, linear algebra and multivariable calculus. We expect students from diverse background, but with a basic level of mathematical maturity. In addition, some familiarity with one of the topic areas: robotics, dynamics, control, vision or graphics is expected. Lectures will be complemented by discussions and presentations by the students in the class. These discussion sessions will help in problem solving.

MEAM 625 Haptic Interfaces for Virtual Environments and Teleoperation . Prerequisite(s):

This is a research-oriented graduate-level class on human haptic sensing, haptic interface design, virtual environment rendering methods, teleoperation control algorithms, and system evaluation.

ESE 650 Learning in Robotics

This course will cover the mathematical fundamentals and applications of machine learning algorithms to mobile robotics. Possible topics that will be discussed include probabilistic generative models for sensory feature learning, Bayesian filtering for localization and mapping, dimensionality reduction techniques for motor control, and reinforcement learning of behaviors. Students are expected to have a solid mathematical background in machine learning and signal processing, and will be expected to implement algorithms on a mobile robot platform for their course projects.

CIS 680 Advanced Topics in Machine Perception. A previous course in machine perception or knowledge of image processing, experience with an operating system and language such as Unix and C, and aptitude for mathematics.

Graduate seminar in advanced work on machine perception as it applies to robots as well as to the modelling of human perception. Topics vary with each offering.

CIS 700 Computer and Information Science Topics.

One time course offerings of special interest.

Departments Affiliated with GRASP