Written by Louis Fernandez, PhD Researcher, based at UTS and part of the Human-Robot Interaction program.

Mathematical optimisation often comes across as intimidating because it’s wrapped in abstract mathematical symbols and notation. If we peel back the equations, what’s the mathematics actually doing in a physical sense? Let’s build an intuitive mental model by looking at how we calculate the minimum distance between two shapes. This problem can be mathematically written as follows:

When you break down an optimisation problem, it comes down to two main components. The first component is the objective function, which simply defines our goal. In our example, the objective function is written as minimise ∥xr − xO∥2. In everyday language, this simply means our goal is to minimise the distance between two points, xr and xO, by adjusting where those points are placed. The expression ∥xr − xO∥2 is the mathematical language for the distance between these two points.

Imagine these two points floating freely anywhere in space (see Fig. 1.1). You’re allowed to move them around however you like to make the distance between them as small as possible. What’s the absolute shortest distance you can get? It’s zero, because you can simply place both points at the exact same location. On its own, this result is trivial, which is why we need rules to make the problem useful.

This brings us to the second component, which are the constraints of the optimisation problem. Constraints set the boundaries and limit how our points move. In our equation, the constraints F (xr) ≤ 0 and F (xO) ≤ 0 act as inside-outside functions.

An inside-outside function F tells you where a point sits relative to a shape. If the point lies outside, F returns a positive value. If it lies inside or right on the surface, F returns a negative value or zero. Because our expression specifies that F ≤ 0, this rule forces our points to stay inside or on the boundary of the shape.  Instead of letting our points float freely anywhere in space, these constraints tie them to real physical objects, such as a robot arm and an obstacle in the environment. We strictly require that the points xr and xO stay trapped inside or on the surfaces of those shapes (see Fig. 1.2).

Now, let’s combine the objective function and the constraints to see the full physical picture. The objective function acts like an attractive force pulling the two points toward each other. At the same time, the constraints act like physical barriers that stop the points from travelling outside the regions defined by the shapes. As the optimisation problem is solved, the objective function pulls the points as close as possible until the constraints stop them at the surface. What the solver ultimately finds is the minimum distance between the two objects (see Fig. 1.3).

1.1 Why Optimisation Matters in Robotics

Hopefully, this mental model gives you a clearer intuition for how mathematical optimisation works in practice. This framework is essential in modern robotics, where calculating distance is rarely as straightforward as applying a basic geometric formula. While simple shapes like spheres have exact analytical formulas for distance, real-world objects require far more complex geometry to be accurately modelled. A robotic arm with multiple joints or a human worker cannot be simply captured by using spheres and ellipsoids. In my PhD research, for instance, I used shapes called superquadrics to represent complex robot links (see Fig 1.4). Mathematical optimisation provides an efficient means of evaluating distances between various robot–obstacle pairs, where the bodies are modelled as superquadrics.

By framing minimum distance checks as an optimisation problem, robots can determine how much space they need to remain safe in real time. For example, a factory robot working alongside people may need to recalculate its distance from nearby workers and obstacles dozens of times per second. By continuously solving this optimisation problem, the robot can monitor its surroundings and respond as conditions change. It can adjust its trajectory, slow down, or stop completely when necessary to prevent a collision. This allows robots to move safely and autonomously in unstructured, human-shared environments.

1.2  Optimisation in Daily Life

While robotics relies heavily on these principles, you actually interact with mathematical optimisation every single day without realising it.

• GPS Navigation: When you ask your smartphone for directions, an optimisation solver can help find the best route to your destination. The objective function might minimise travel time or the number of toll roads used, while the constraints include the available road network, speed limits, one-way streets, and current traffic conditions.
• Smart Home Thermostats: A smart heating controller balances comfort against energy costs. The objective function minimises electricity usage, while the constraints ensure the room temperature stays within your preferred comfort zone despite the weather outside.
• Delivery and Logistics: Courier services must determine the most efficient sequence for a driver to visit dozens of delivery locations. The objective function minimises fuel consumption and distance driven, constrained by delivery time windows and vehicle cargo capacity.

Once you view the world through this lens, optimisation stops looking like intimidating equations on a whiteboard. It becomes a practical tool for finding the best possible solution while respecting the physical rules of the world around us.

Written by PhD Researcher, Jasper Vermeulen, Designing Socio-Technical Robotic Systems program.

When people think about Human-Robot Collaboration, they often imagine a worker and a robot side by side, completing a task together. This image has shaped much of the discussion around collaborative robotics. It is simple, compelling, and often useful.

However, new research suggests that this picture may be incomplete.

In practice, successful Human-Robot Collaboration rarely depends on the worker and robot alone. It is often made possible by a wider network of people who configure, supervise, maintain, troubleshoot, adapt, and support the robotic system over its lifetime. While attention naturally focuses on the person closest to the robot, collaboration is often sustained by many others whose work is less visible but equally important.

In this sense, Human-Robot Collaboration is not only about how humans and robots work together. It is also about how people work together around robots.

Moving Beyond the Human-Robot Pair 

Collaborative robots, or cobots, are often introduced with the promise of combining the strengths of humans and machines. Humans contribute flexibility, judgement, and problem-solving capabilities, while robots contribute precision, consistency, and ergonomic support.

This vision has been enormously valuable in advancing collaborative robotics. Yet it can also encourage us to focus primarily on the interaction between a single worker and a single robot.

Real workplaces are rarely that simple.

In manufacturing environments, successful cobot deployments often involve operators, supervisors, technicians, engineers, safety specialists, and system integrators. While these individuals may not always work directly alongside the robot, they play important roles in enabling effective collaboration.

The result is that Human-Robot Collaboration is often still dependent on Human-Human Collaboration.

The People Behind the Robot 

Consider what happens when a cobot is introduced into a production environment.

Someone needs to configure and integrate the system. Someone needs to train workers. Someone needs to monitor performance, troubleshoot problems, and adapt workflows when unexpected situations arise. As production requirements evolve, someone must ensure that the robot continues to support organisational goals while remaining useful to workers.

These contributions are essential, yet they often receive far less attention than the technology itself.

In many organisations, individuals naturally emerge who help bridge the gap between human work practices and robotic capabilities. They may be engineers, technicians, supervisors, or experienced operators. Informally, they often become what some practitioners call “robot wranglers”: people who help make collaboration work in practice.

Their work matters because collaborative robots do not enter workplaces as isolated technical tools. They become part of existing routines, responsibilities, relationships, and constraints. Making them work well requires more than programming the robot. It requires ongoing coordination between people.

Designing for Teams, Not Just Isolated Users 

Industry 5.0 makes this explicit: technology should be designed around people, not the other way around. This shift recognises that successful technology adoption depends not only on technical performance but also on human experience and organisational context.

Collaborative robotics should therefore not be viewed solely as a relationship between a worker and a robot. Instead, it should be understood as part of a broader socio-technical system involving multiple people, shared responsibilities, and coordinated expertise.

This has important implications for organisations considering cobot adoption. Investing in robotic technology is only one part of the equation. Equally important is investing in the people who support, maintain, adapt, and champion that technology over time.

This also matters for design. If collaborative robots are part of team-based work, then future systems may need to support more than the immediate operator. They may need to make system status clearer to supervisors, troubleshooting easier for technicians, handovers smoother between workers, and adaptation more accessible to the people responsible for keeping production moving.

What’s Next? 

As robots become increasingly common across manufacturing and other industries, we may need to rethink how we define collaboration itself.

Rather than asking only how a human and a robot can work together, perhaps we should also ask how teams of people work together around a robot.

This raises several important questions:

• Who are the hidden contributors supporting Human-Robot Collaboration within your organisation?

• Are organisations investing enough in the people who help make cobot deployments successful?

• How might future robotic systems be designed to support entire teams rather than individual users?

After all, the future of collaborative robotics may not be about replacing human expertise. It may be about understanding how robotic technologies become part of successful human teams.

Human-Robot Collaboration may begin with a human and a robot, but it succeeds through the people who make that collaboration possible.

Written by Dr. Katia Bourahmoune, Acting Co-Lead, Quality Assurance & Compliance program. 

In April 2026, a humanoid robot crossed the finish line of a Beijing half-marathon in fifty minutes and twenty-six seconds, faster than any human being has ever run that distance [1]. Months earlier, humanoid robots had performed incredibly complex, synchronized martial arts routines [2]. As the media coverage gained widespread attention, something more interesting than this engineering achievement emerged: a question, not yet fully formed, about what kind of world we are now entering, and whether we are entering it with our eyes open. 

The choice to build robots in the human form is sometimes caricatured as a vanity of engineers or a concession to popular culture and science-fiction media, however, its philosophical wager is of considerable depth. The world into which these machines are being released (its factories, hospitals, construction sites, and even homes) was designed for users that stand upright, use two hands, and react dynamically to the world around them. 

Traditional forms of industrial and collaborative robots were built for tasks in bounded environments, e.g. a wheeled platform optimised for a warehouse floor or an articulated arm for a single weld point on an assembly line. A humanoid robot carries an inherent optimism about general physical intelligence: the bet, or perhaps ambition, that a machine capable of inhabiting the full texture of human environments can in time respond to the full texture of human need. The ancient concept of Ziran in classical Chinese thought illuminates what the designers in this field are reaching toward. Ziran is often rendered as naturalness, or the disposition of things to accord with their own nature [3]. In the context of robotics, this can be found in the idea of building machines that fit the world as it is, rather than demanding the world be remade to fit the machine. 

Humanoid robots are now operating in production environments and shipping in volumes that would have seemed premature as recently as 2023. Venture capital investment in humanoid robotics exceeded three billion dollars in 2024, with reports of multi-billion market projections for the next decade [4]. What this momentum cannot easily tell us is whether the design assumptions underlying this transition have been adequately examined. The present dominant commercial logic treats humanoid forms primarily as a means of fitting machine labour into existing human infrastructure i.e. same floor plan, same tools, and minimal workflow redesign. That is a reasonable engineering position. It may also be eclipsing, earlier than is wise, questions around whether the humanoid is best understood as a substitute for human presence or as a platform for augmenting it. 

It is worth noting that the world these machines are being designed to inhabit was itself built around the human body. Every dimension of that infrastructure, accumulated across two centuries of industrial development, was calibrated to the physical limits and capabilities of the biological human form. While previous waves of automation reshaped work around the machine, the humanoid, at least in aspiration, inverts that relationship. In doing so, it raises a concern that the industrial revolution never had occasion to face: What becomes of the human body’s centrality to working life when the physical form that justified building the world around it can be replicated, scaled, and indefinitely reproduced? That this question is now being asked simultaneously in boardrooms, parliaments, and papal encyclicals is perhaps the clearest measure of its weight [5].  

What the field of collaborative robotics has understood for some time (and what the humanoid moment is now forcing into general visibility) is that matching human physical capability, however necessary, is not sufficient. Harder questions concern the relationship between human and robot: what kind of human-robot partnership produces durable, humane, and useful outcomes, and under what conditions workers can reasonably extend trust to machines working beside them. Those questions shaped decades of research into human-robot interaction and collaboration and the work the Australian Cobotics Centre has been part of since 2021. How much humanoids come to define the next chapter of that work is ultimately a question research and humanity will have to answer. 

Call for Participation

The Australian Cobotics Centre is calling for experts across academia, industry, and government to participate in a research study at the University of Technology Sydney aimed at developing a clearer definition of collaborative robots. Participation involves an online discussion followed by a brief activity to rate statements about cobots. Your input will directly inform how the field defines and frames human–robot collaboration. 

More information and EOI here:  EOI and Consent Form (https://forms.office.com/r/YSYQPWqD8X) 

References and Further Reading:  

[1] Harmon, K. (2026). A humanoid robot beat the human half-marathon record at a Beijing race. But what did it actually prove? Scientific American.  

[2] Unitree Robotics. (2026). Kung fu meets spring: Unitree Spring Festival Gala robots present “Cyber Real Kung Fu” in the year of the horse [Press release]. PR Newswire.  

[3] Cleary, T. (Trans.). (1992). The essential Tao: An initiation into the heart of Taoism through the authentic Tao Te Ching and the inner teachings of Chuang-tzu. HarperCollins.  

[4] Goldman Sachs. (2024). Humanoid robots: A $38 billion market by 2035. Goldman Sachs Research.  

[5] Leo XIV. (2026). Magnifica Humanitas [Encyclical letter]. Dicastery for Communication, Holy See.