Load, Swing, Strike: Optimal Control of Robots Exploiting Elastic Tool Dynamics

When you swing a hammer, axe or fishing rod, you do not simply drive it along a planned path. You store energy in the tool and in your own tendons, then release it at the right moment. Robots rarely use tools this way. Our project will develop the optimal control theory that allows them to.

Why it matters

Robots are designed and controlled to be stiff and precise. Flexibility in a joint, link or held tool is treated as a disturbance to suppress, and motion is servoed to a planned trajectory. This works well for repetitive factory tasks, but not for striking, cutting, shaking or scraping, where speed, force and endurance matter more than accuracy.

These tasks are central to inspecting and maintaining bridges, tunnels, ship hulls and wind turbines, to construction and to agricultural harvesting, often in places not designed for machines. Robots that exploit stored elastic energy and passive tool dynamics, as people do, could carry out this work faster, more efficiently and more robustly.

What we know

Elasticity is known to help in explosive tasks: robots with variable-stiffness actuation have struck and thrown faster than rigid designs. For repeated motions, nonlinear normal modes have been used to produce efficient oscillations, and iterative learning control has refined the motion of flexible arms over repeated trials. Preliminary work shows that a swing optimised to load and release a flexible tool strikes faster than one planned as if the tool were rigid.

What is missing

However, most of these results apply to simple models or a single task, depend on hand-tuned parameters, and find one locally optimal solution with no guarantee of its quality. They are also fragile: change the tool, load or contact and the solution must be recomputed or relearnt. Impacts and intermittent contact, central to tool use, are often simplified or ignored.

Research questions

Our project will address these gaps by developing optimal control methods that plan the storage and release of energy, not only position. You will explore questions such as:

• How can optimal swinging, striking and repetitive motions be computed for robots using elastic tools, at realistic scale and with guarantees on convergence or optimality?

• How does an optimal motion degrade when the tool, load or contact changes, and how can it be recovered without starting again?

• How should impacts and intermittent contact be modelled so that they form part of the optimisation?

• Which joint, grip or tool compliance makes optimal behaviour naturally robust?

The same ideas apply to legged locomotion, where every footstep is an impact, and you may take the work in that direction.

How you will do it

The work is theory-led and mainly simulation-based. You will use nonlinear and hybrid dynamic modelling, trajectory optimisation and numerical continuation, with machine learning where it helps. You will test key results on laboratory robot arms swinging instrumented flexible tools, using high-frequency Vicon motion capture to record their response, and compare the robot with people performing the same tasks.

Who you will work with

You will be supervised by Dr Peter Hubbard, Senior Lecturer in Control Systems Engineering, whose research covers optimal control, trajectory optimisation and estimation, with recent work on motorcycles, energy-efficient electric vehicles and wheel–rail friction. Peter meets his students regularly and encourages them to shape their own research direction.

You will join the Intelligent Control Systems group in the Wolfson School and work alongside the Intelligent Automation Centre's collaborative robotics group, which studies how robots can apply high forces and use tools safely. Facilities include industrial and collaborative robot arms (Universal Robots, KUKA, ABB), motion-tracking systems and an instrumented human-robot workspace.

What you will gain

• Expertise in optimal control, nonlinear dynamics and numerical optimisation, using tools such as CasADi, MATLAB and Python.

• Experience of testing theory on real robots with motion capture.

• Opportunities to publish in leading robotics and control journals and conferences.

• Skills valued in academic and industrial careers in robotics, automation and autonomous systems.

Funding

This PhD project is open to self-funded applicants. Many of the Doctoral Researchers at Loughborough University are supported through a range of funding routes, including external funding bodies, government scholarship schemes and employer sponsorship. Further information on funding opportunities is available on the Research degree funding webpage.

Applications are particularly welcomed from candidates who can secure external sponsorship through competitive funding schemes, such as the Commonwealth Scholarships Commission or the China Scholarship Council (CSC).

Loughborough University has an applied research culture. In REF 2021, 94% of the work submitted was judged to be top-rated as 'world-leading' or 'internationally excellent'.

We are a community based on mutual support and collaboration. Through our Doctoral College there are continual opportunities for building important research skills and networks among your peers and research academics.