Physics

Control engineering

Human–robot interaction

Aerospace engineering

Mathematics

Agronomy

Biology

Human–computer interaction

Mathematical optimization

Engineering

Artificial intelligence

Economics

Systems engineering

Controller (irrigation)

Microeconomics

Game theory

Control (management)

Observer (physics)

Differential game

Computer science

Task (project management)

Quantum mechanics

Simulation

Control theory (sociology)

Robot

Differential (mechanical device)

Nature Machine Intelligence

The last decades have seen a surge of robots working in contact with humans. However, until now these contact robots have made little use of the opportunities offered by physical interaction and lack a systematic methodology to produce versatile behaviours. Here, we develop an interactive robot controller able to understand the control strategy of the human user and react optimally to their movements. We demonstrate that combining an observer with a differential game theory controller can induce a stable interaction between the two partners, precisely identify each other’s control law, and allow them to successfully perform the task with minimum effort. Simulations and experiments with human subjects demonstrate these properties and illustrate how this controller can induce different representative interaction strategies. Robots need to estimate and adapt to human behaviour, especially when human dynamics change over time. Now adaptive game theory controllers can help robots adapt to human behaviour in a reaching task.

Differential game theory for versatile physical human–robot interaction