Arthur Richards : Research

Information on my research is being migrated to the Aerospace Guidance and Control pages.

NEW Receding Horizon Control with Learning

Final year student Patrick Boyle

This project extends Robust Safe Receding Horizon Control (RSBK) so that the cost-to-go approximation is developed by a process based on Reinforcement Learning. The same robust constraint satisfaction properties are inherited from RSBK, but the method can now learn generic problems and costs, including risk or height penalties as well as distance.

Click the picture on the right to view a movie simulation of the method, learning a shortest path obstacle avoidance problem, as a comparison example. The path taken in each trial (top) has random exploration initially but converges to a good solution. The path history is shown in the middle plot, and the cost evolution can be seen in the botton two plots.

Planning and learning video

(click to play MPG movie)

UPDATED Robust Model Predictive Control

Final year students William Stewart and Alex Wilkinson

Model Predictive Control (MPC) naturally handles systems with constraints, and has become very popular in the process industry. With robustness techniques such as constraint tightening or policy optimization, constraint satisfaction can be guaranteed up to specified disturbance levels. This project has employed a new Simulink and dSpace implementation of MPC for the control of an aerospace system. A new warm-start facility was added to the optimizer to achieve fast operation.

The picture on the right shows a model aircraft in a wind tunnel, with MPC used to keep it within the constraints marked by the red lines of tape. From top-to-bottom, the graphs show the swing angle, elevator control, and applied disturbance. In the movie (click picture to play WMV) the control can be seen to become much more aggressive as the aircraft nears and then rides the constraint, before the disturbance becomes too much and the constraint is exceeded. Click the following links for more photos: the aircraft in the wind tunnel : another aircraft shot : an initial hardware-in-the-loop MPC experiment : a close-up of the HITL oscilloscope trace

Aircraft MPC video

(click to play WMV movie)

NEW Terrain Avoidance for Helicopters

PhD Student Colin Greatwood, supported by EPSRC and QinetiQ

Helicopters are often called upon for low-level flight in limited visibility, increasing the risk of flight into terrain or obstacles. This project aims to analyse the region or "bubble" with which the helicopter might overlap, and exploit this information to develop smart sensing and navigation systems.

The picture on the right shows the bubble for an initial simplified 2-D model of a helicopter in slow forward flight. Click the picture to view an MPEG movie illustrating how the bubble changes shape and location through a simple manoeuvre.

Reachable set

(click to play movie)

UPDATED Branch-and-Bound Optimisation for Collision Avoidance

PhD Student Alison Eele, supported by EPSRC

This research involves a new approach to finding globally optimal solutions to avoidance problems, including UAVs avoiding radar threats and civil aircraft avoiding each other in free flight ATM. It is faster than existing methods, because it can incorporate geometric knowledge in the optimisation algorithm instead of buying an expensive "black box" optimiser. It can also include more realistic, nonlinear dynamics models. Furthermore, we are researching "hot start" methods for updating paths in the light of new information. Most existing work in this area simply restarts the optimisation from scratch.

Click the picture on the right to view an MPEG movie illustrating the branch-and-bound search process for a typical problem. Click the following links for more example cases: 30 obstacles : escaping a dead-end : turning to a target behind the start : overlapping obstacles


(click to play movie)

UPDATED Optimisation of Aircraft Taxi Operations

PhD Student Gillian Clare (nee Keith), supported by EPSRC and Airbus UK. This project is part of the Knowledge Transfer Network for Industrial Mathematics.

Future growth of air traffic demands faster air-to-gate-to-air transit at airports and the ICAO Advanced Surface Movement Guidance Control System specifically identifies the "routing" function as an opening for future autonomous operation. This project aims to apply advanced, robust, non-convex optimisation tools to the taxi routing problem, in order to reduce transit times, increase throughput capacity, and improve safety.

Click the picture on the right to view an MPG movie illustrating an optimized solution for six aircraft taking off from runway 27R at London's Heathrow Airport. Note how aircraft 6 moves aside, off its direct path to the runway, to allow aircraft 3 to pass. This optimization combines routing, timing and runway scheduling problems into one.

Click here for another example movie (3.5MB WMV) showing a much larger problem: 39 aircraft movements at Heathrow, including one token arrival. This example uses a receding horizon optimization of the aircraft routing and timing, with iterative constraint application to reduce the computation required.


(click to play movie)

UPDATED Adaptive Navigation in Uncertain Urban Environments

Postdoctoral research assistant Markus Deittert, supported by Systems Engineering for Autonomous Systems Defence Technology Centre in collaboration with BAE Systems

Click the picture on the right for a movie demonstrating "adaptive navigation", combining receding horizon control with Simultaneous Localisation and Mapping (SLAM). A vehicle (green circle or triangle) must navigate to its goal (green or blue square) while avoiding the walls (red lines). However, the vehicle has no GPS or equivalent, nor does it know where the walls are. It must build a map by sensing the walls and update its plans as it goes. The current project will perform experimental testing of the algorithms on BAE's indoor Pioneer and outdoor Wildcat robotic vehicle platforms.

Top left: truth display. Top right: current measurements, including ranges (blue dots), wall segments (red lines) and feature points (squares). Bottom left: map model, including estimated walls (red lines), vehicle location and path (blue line), feature point estimates (blue ellipsoids) and goal location (blue square). Bottom right: plan display, including near-term detailed plan (blue line), far-term approximate plan (purple dashed line), current visible region (yellow) and cell-based world model (green).

Adaptive Navigation Example Movie

(click to play 5.7MB MPG movie)

Cooperative Distributed Model Predictive Control

PhD Student Paul Trodden, supported by EPSRC and BAE Systems

Decentralized Model Predictive Control (DMPC) solves a separate planning problem for separate subsystems but ensures satisfaction of coupled constraints. Breaking up the problem results in significant reductions in computation time, compared to solving a single planning problem for the team. Careful choice of the objective function improves performance using cooperative behaviour instead of "greedy" actions.

Click the picture on the right for a movie demonstrating the difference between ordinary "greedy" DMPC and cooperative DMPC. Two vehicles must pass to reach their targets (circles) but the passage is too narrow. Beginning with greedy DMPC, the two vehicles reach a deadlock, but when they switch to cooperative DMPC, the deadlock is broken and both reach their targets.

DMPC Example Movie

(click to play 1.5MB MPG movie)

Autonomous Vehicle Testbed

These robot vehicles are being developed for use in future projects. Rovers like these are used for testing and development of vehicle control algorithms. They have on-board computers, wireless network communications, and position sensing capability. They also have room for future upgrades including fitting on-board cameras or GPS for outdoor operations.


(click to enlarge)

Robust Safe Receding Horizon Control

Work done in conjunction with the Aerospace Controls Lab, MIT

"Receding Horizon" control here means that the vehicle only plans for part of its trip to the goal, and uses a simple cost function to represent the remainder of the mission. This greatly reduces computation time. "Safety" means that there is a guarantee that the vehicle will never hit an obstacle, even if it discovers that there is no path to the goal. In the figure on the right and the animations (see links below) the vehicle is repesented by a triangle, the boxes are the obstacles, the green circle is the sensor range for the vehicle and the red obstacles are those known to the vehicle, i.e. if they have a corner within the green circle. The purple boxes are the planned "tube", a sequence of invariant sets that the vehicle can follow despite the disturbances. This result is part of on-going research on designing robust planning controllers, with a focus on offering rigorous guarantees of properties, such as stability, constraint satisfaction, and target reaching, despite the presence of uncertainties.

Some MPEG movies of example simulations : Example 1 : Example 2 : Example 3 : Example 4


(click to enlarge)

Path Planning for Nap-of-Earth Flight

Final year students Gillian Keith and James Tait

The figures on the right show two views of a trajectory for nap-of-earth flight, i.e. as low as possible, avoiding terrain. Like most avoidance problems, it is non-convex and therefore difficult to find the globally optimal solution. In this case, the problem has been recast as a Mixed-Integer Linear Program (MILP) using a new representation for 3-D terrain representation. Results show that this new method, combined with techniques for terrain simplification and enhanced MILP solution, offers significantly faster computation compared to state-of-the art methods.

Movie (MPEG format) of two vehicles flying optimized nap-of-earth trajectories. Blue minimizes total distance and therefore goes up and over the terrain. Green minimizes integrated altitude and takes a less direct route, staying low in the valley.Click here. Netscape users: right click and save.

Trajectory isometric view

Trajectory plan view

(click to enlarge)

Robust Distributed Model Predictive Control

Work done at the Aerospace Controls Lab, MIT

The figure on the right shows a simulation of six Unmanned Aerial Vehicles. Each must reach its goal (blue circle on the right) without colliding with the others. Decentralized Model Predictive Control solves a planning problem for each UAV separately but still guarantees arrival and collision avoidance. Breaking up the problem results in a five-fold reduction in computation time, compared to solving a single planning problem for the team.

Some MPEG movies of other simulations : Four UAVs : Five UAVs : Six UAVs : Seven UAVs


(click to enlarge)

Robust Control of UAVs with Obstacle Avoidance

Work done at the Aerospace Controls Lab, MIT

Robust predictive control is combined with obstacle avoidance to guarantee that UAVs reach their goals while avoiding obstacles. The figure (click to enlarge) shows ten simulations, each with random disturbances (like wind) acting on the vehicle. It starts at the left, and always reaches its goal, the green box on the right, while avoiding the obstacles (red). Note how the UAV takes quite different routes depending on the disturbance.

Some MPEG movies of other simulations. Each movie shows ten UAVs (as purple dots) with the same controller but with different disturbances : Movie 1 : Movie 2 : Movie 3 : Movie 4 : Movie 5 : Movie 6

Trajectory example

(click to enlarge)

Spacecraft Trajectory Optimisation with Plume Avoidance Constraints

Work done at the Aerospace Controls Lab, MIT

The figure on the right shows two solutions for the same reconfiguration of a formation of three spacecraft. In the left hand figure, the initial thruster burns (marked by red lines) impinge upon other spacecraft in the formation. In the right hand figure, constraints have been added to prevent this impingement. The reconfiguration strategy is quite different to the right hand figure, with one spacecraft setting off in completely the opposite direction. The thruster burns do not impinge on the spacecraft, and the maneuver is known to be the minimum fuel reconfiguration without plume impingement.

Movie (Windows AVI format) of simulated space station close-up inspection maneuver with plume impingement avoidance. Note final approach ensures that the braking thrust does not hit the station. Click here. Netscape users: right click and save.

Spacecraft Plume Impingement

(click to enlarge)