Multi-surface sliding mode control of continuum robots with mismatched uncertainties

In this paper, we tackle the control problem of continuum robots with mismatched uncertainties. Uncertainties that affect systems through any of their states and may not be directly accessed by their controllers. These uncertainties emerge in a system either due to unmodeled dynamics, practical limitations, or external disturbances. Continuum robots possess highly nonlinear dynamic behaviour due to their elastic nature and operate within undefined or congested environments, exposing them to such uncertainties. However, mismatched uncertainties in the continuum robots’ field, are yet to be addressed. Here, we tackle this problem and propose the first robust control for continuum robots that assures its robustness property under mismatched uncertainties. To this end, we first derive the dynamic model for our continuum robot by considering it as an elastic rod and then applying Cosserat rod theory. This will result in a general dynamic model that does not require any design or operative assumption. Next, we design our robust controller utilizing multi-surface sliding mode control, a method capable of handling nonlinear systems under mismatched uncertainties. Finally, we include simulations to validate our controller’s performance.