Robust force–position control of a novel DAE model for position servo-actuated robot manipulators

The operation of robot manipulators requires continuous interaction with their environment, particularly in tasks such as assembly or delicate manipulation, where robots must apply a specific force to an object or surface without exceeding predetermined limits. When a robot manipulator interacts with an environment that does not deform or is assumed to be infinitely rigid, differential algebraic equations (DAE) are used to simplify the modeling process. In such cases, hybrid controllers have been proposed to simultaneously control position and force for robots equipped with ideal torque actuators, i.e., robots for which the input signals are treated as desired torque or force reference signals for their actuators. However, this assumption is often unrealistic, as most robots intended for applications requiring high-precision motion control are actually equipped with position servomotors, which require position input signals for the robot’s actuators. Therefore, in this work, we propose a novel DAE model for position servo-actuated robot manipulators under contact constraints. Additionally, we introduce a force–position control strategy based on the orthogonalization method and integral sliding modes, which guarantees the convergence of position and force errors while considering time-varying trajectories. Stability of the closed-loop system is concluded via the Lyapunov method. Finally, simulations of a three degrees of freedom robot manipulator corroborate the effectiveness of our proposal. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.