Motion Planning in Autonomous Robots

Information on this PhD research area can be found further down this page under the details about the Widening Participation Scholarship given immediately below.

Applications for this PhD research are welcomed from anyone worldwide but there is an opportunity for UK candidates (or eligible for UK fees) to apply for a widening participation scholarship.

Widening Participation Scholarship: Any UK candidates (or eligible for UK fees) is invited to apply. Our scholarships seek to increase participation from groups currently under-represented within research. A priority will be given to students that meet the widening participation criteria and to graduates of the University of Salford. For more information about widening participation, follow this link: https://www.salford.ac.uk/postgraduate-research/fees. [Scroll down the page until you reach the heading “PhD widening participation scholarships”.] Please note: we accept applications all year but the deadline for applying for the widening participation scholarships in 2024 is 28th March 2024. All candidates who wish to apply for the MPhil or PhD widening participation scholarship will first need to apply for and be accepted onto a research degree programme. As long as you have submitted your completed application for September/October 2024 intake by 28 February 2024 and you qualify for UK fees, you will be sent a very short scholarship application. This form must be returned by 28 March 2024. Applications received after this date must either wait until the next round or opt for the self-funded PhD route.

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Project description: The project will focus primarily on Autonomous Robots: The general research theme involves theoretical and experimental study of Autonomous Vehicles with emphasis on advanced motion control for unmanned vehicles. This includes control of highly manoeuvrable and underactuated vehicles, collision avoidance methods, and formation control. Considered motion control scenarios include target tracking as well as path following, tracking, and manoeuvring.

Hamiltonian systems and Lie group geometry are natural mathematical tools in this setting. This enables one to plan large manoeuvres using an optimal controller. Current applications and motivations include:

·      Spacecraft attitude problem – Controlling the orientation of a satellite is a well known problem. Firstly, the problem of reconfiguration where the satellite is maneuvered from an initial to final configuration. This problem can be tackled using optimal control while minimizing some practical cost function. In addition at equilibria, we may wish to stabilize the motion of the satellite. The Lie group framework can tackle this entire problem globally.

·      Autonomous Underwater Vehicles (AUV) - The motion planning problem of an AUV has received much attention in recent years, as a result of a growing industry in underwater vehicles for deep sea exploration or ship inspection for maintenance on ship hulls. For an underwater vehicle to succeed it must be able to control its own motion while minimizing the amount of fuel required to perform its task. As in the spacecraft attitude problem we wish to design global optimal controls for these systems as well as use geometric techniques to stabilize its motion while minimizing fuel usage.

Affine control systems defined on finite dimensional Lie groups form an important class of nonholonomic control system that provide a mathematically rich setting for studying mechanical systems. These mechanical systems include the motion control of autonomous systems (underwater vehicles, wheeled mobile robots, aircraft, helicopters, and spacecraft). This research encompasses theoretical and new developments in the area of motion control of autonomous vehicles, with an emphasis on global motion planning. This research use mathematical equations to describe the kinematics of the system and the Maximum principle of optimal control to derive the equations of motion for the autonomous vehicles.  For systems defined on Lie groups these equations can be expressed in a coordinate free manner and therefore analysis of these equations are global. The global analysis then comprises of the following:

·      Tracking and path-following of autonomous vehicles.

·      Identify globally defined equilibrium solutions. This avoids the use of complicated numerical techniques to identify periodic/bounded equilibria.

·      Stability of equilibria.

The project will focus primarily on an Underwater Vehicles: The general research theme involves theoretical and experimental study of Underwater Vehicles with emphasis on advanced motion control for unmanned marine vehicles. This includes control of highly manoeuvrable and underactuated vehicles, collision avoidance methods, and formation control. Considered motion control scenarios include target tracking as well as path following, tracking, and manoeuvring.

Additional Information

The successful applicant should have been awarded, or expect to achieve, a Masters degree in a relevant subject with a 60% or higher weighted average, and/or a First or Upper Second Class Honours degree (or an equivalent qualification from an overseas institution) in Bachelors or Masters Degree with mathematics and physics as major subjects. Preferred skill requirements include knowledge/experience of Hamiltonian Mechanics, Group Theory, Topology, Geometry.