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Aims:

The aims of this module are to:

• Provide students with a solid grounding to apply basic mathematical techniques for control in the solution of problems in the domain of robotics and AI.
• Support students to predict system stability under varying conditions based on mathematical or numerical analysis.
• Provide students with the theoretical and practical enabling knowledge in fundamental concepts in control as applied to simple robots with embedded processors.
• Support students to problem solve so that they can analyse and decompose problems in robotics into appropriate control subsystems.
• Support students to develop a holistic understanding of the practical application of theory and foundational knowledge of AI –based robotic systems (project).
• Build students’ confidence when liaising with and presenting in future industrial contexts, working with peers and participating in AI–based robotics projects.

Intended learning outcomes:

On successful completion of the module, a student will be able to:

1. Describe simple approaches to control and reason about their advantages and disadvantages.
2. Describe feedback control systems using mathematical techniques, transferring functions and state space models.
3. Analyse the stability properties of simple control systems so described, using both mathematical and computational techniques.
4. Design and build simple control systems in simulation and reality with given expected properties and integrate these design components into robotic platforms, testing this to ensure operability.
5. Demonstrate and assess the performance of the system, improving it where appropriate.
6. Model these systems mathematically and find solutions to these models.
7. Identify and demonstrate a critical understanding of the role that control knowledge plays in the development and build of AI-based robotic systems.
8. Demonstrate engagement with reflective and learning as key academic and professional skills.

Indicative content:

To effect predictable and repeatable changes in robotic systems that move an algorithm that controls the system’s actuators given input from sensors is essential. This is an introductory module that covers some of the fundamental mathematics that underpins reasoning about control systems, descriptive techniques that allow one to understand control performance and the engineering of practical control systems. This introductory module is part theory and part a practical use of that theory.

The following are indicative of the topics the module will typically cover:

• Models (predictive model, discrete vs continuous time).
• Simple control techniques: bang/bang, PID control.
• Control of wheeled robots.
• State space models.
• Linearisation, LTI systems.
• Laplace Transform, z transform.
• Transfer Functions.
• Stability.
• Reachability and Observability.
• Bode Plots, gain and phase margins.
• Indicative topics in calculus (Taylor and Maclaurin series, ODEs, differentiation under an integral, Jacobians.)

Requisites:

To be eligible to select this module as optional or elective, a student must: (1) be registered on a programme and year of study for which it is a formally available; and (2) have completed Mathematics for Robotics and Artificial Intelligence 1 (COMP0202) and Introduction to Mechanical Systems (COMP0203) in Term 1.