## Theme: Robotics, Control Theory and Systems

Tracing its origins to J. C. Maxwell’s early work on speed governors (1868), control theory has evolved to play an integral role in the majority of modern engineering systems. Mechanical systems are becoming ever more complex, yet performance requirements are increasingly stringent. At the same time, dramatic developments in microelectronics and computers over the past few decades make it possible to use sophisticated signal processing and control methodologies to enhance system performance.

This theme addresses the broad spectrum of control science and engineering from mathematical theory to computer implementation. On the application side, research teams are engaged in projects involving a variety of mechanical systems such as robot manipulators, manufacturing systems, vehicles and intelligent vehicle highway systems (IVHS), motion control systems, computer storage devices and biomedical systems. Berkeley prides itself on the tradition of nurturing the delicate balance between the theoretical and applied aspects of research. The control group has taken the lead in the field of mechatronics and IVHS integrating electromechanical/machine-information.

##### Robotics, Control Theory and Systems Microcourses

#### E251: Model Predictive Control for Autonomous systems – Introduction

#### E254: Model Predictive Control for Energy systems – Introduction

Forecasts are fundamental in the new generation of autonomous and semi-autonomous systems. Predictions of systems dynamics, human behavior and environment conditions can improve safety and performance of the resulting system. Predictive control is the discipline of feedback control where forecasts are used change in real time the behavior of a dynamical system. Optimization-based control design is highly requested skill from a number of industries, including energy automotive, aerospace, process control and manufacturing. This course covers the basic design of SISO and MIMO and predictive feedback controllers for linear and nonlinear systems. The student will be exposed to how to apply predictive control design and analysis tools to classical and modern control problems with application to energy systems including solar power plant and energy storage systems.

#### E250: Feedback Control for Linear Systems

This course provides a brief overview of the basic concepts in linear systems and feedback control. The course begins with an exploration of the feedback control problem and its applications in various fields: robotics, manufacturing, traffic, etc. We will present the unifying mathematical formulation of the problem, as well as its fundamental concepts: equilibrium and stability. We then explore the application of these concepts to linear systems and the role of linear algebra. With a grasp of the range of possible behaviors of linear time-invariant systems, we proceed to the design of feedback controllers. In the second session of the course we talk about output feedback techniques. We consider the influence of proportional and integral action, and we put these together in a worked example using PID control. This example illustrates the limits of PID and motivates the third session on state feedback methods. In the third session we describe the pole placement approach to state feedback, and couple it with the analogous state estimator. We briefly discuss observability and controllability as prerequisites for this design approach. We end the course by solving the example of the previous session with state feedback techniques, and motivating other advanced topics in control theory.

#### E253: Flying Robots: from Small Drones to Aerial Taxis

Aerial robots are increasingly becoming part of our daily lives. This course is aimed at a broad audience and intends to give an introduction to the main considerations made when designing aerial robots. We will consider sizes ranging from less than 1 kilogram to vehicles that can carry multiple passengers. Using simple physics, we will derive some fundamental constraints and trade-offs. We will also discuss autonomy of such systems, and specifically different components used in the sense-decide-act feedback control loop.

#### E252: Legged Robots: How to make Robots Walk and Run

Bipedal robot locomotion is a challenging problem. This course will introduce students to the math behind bipedal legged robots. We will cover modeling and dynamics of legged robots, trajectory planning for designing walking and running gaits, and common control strategies to achieve the planned motions. The course will also include applied techniques of programming up a simulator with a dynamical model of a bipedal robot as well as a controller that stabilizes a walking gait. This short course will take students through every step of the process, including:

― Mathematical modeling of walking gaits in planar robots.

― Analysis of periodic orbits representing walking gaits.

― Algorithms for synthesizing feedback controllers for walking.

― Algorithms for optimizing energy-efficient walking gaits.

― Detailed simulation examples.