Soft robots are increasingly being explored and developed in various settings that demand safe and adaptable interactions between robots and their environments. In addition, soft robots exhibit passive compliant behaviour and generate continuous deformations when engaging with the environments. This imposes challenges on achieving active, on-demand interaction force control, especially when feedback force sensing devices are not available. Consequently, there is a need to explore new model-based force control paradigms for soft robots. In this paper, we propose a (quasi-)static force control approach for soft robots based on the compliance modelling, avoiding the necessity for feedback control loops or extensive training data collection. The proposed approach can deliver contact force control along three
Cartesian axes when the robot is actuated into various configurations. The compliance matrix is derived with the robot configuration, which allows the calculation of desired deflection displacements needed to generate on-demand forces. The resulting force control is achieved by solving inverse kinematics problems based on these deflection displacements. The efficacy of our proposed controller is validated through experiments with both one- and two-segment pneumatic-driven soft continuum robots. The
results demonstrate effective static force control performance, with mean control errors below 5% of
the desired peak forces.