Combined Adaptive and Predictive Control for a Teleoperation System with Force Disturbance and Input Delay

Abstract

This work presents a new discrete-time adaptive-predictive control algorithm for a system with force disturbance and input delay. This scenario is representative of a mechatronic device for percutaneous intervention with pneumatic actuation and long supply lines which is controlled remotely in the presence of an unknown external force resulting from needle-tissue interaction or gravity. The ultimate goal of this research is the roboticassisted percutaneous intervention of the liver under Magnetic Resonance Imaging (MRI) guidance. Since the control algorithm is intended for a digital microcontroller, it is presented in the discrete-time form. The controller design is illustrated for a 1 degree-offreedom system and is conducted with a modular approach combining position control, adaptive disturbance compensation, and predictive control. The controller stability is analyzed and the effect of the input delay and of the tuning parameters is discussed. The controller performance is assessed with simulations considering a disturbance representative of needle insertion forces. The results indicate that the adaptive-predictive controller is effective in the presence of a variable disturbance and of a known or variable input delay.

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

“…Conversely, with 2 = 0 this is only possible if 1 = 0, which would however prevent the convergence of 1 to zero. This represents an advantage of the proposed approach in comparison to more traditional predictive control algorithms [18].…”

“…This is in agreement with the fact that the relative weight of the corrective term in (13) increases with the input delay, as pointed out in Remark 2. Notably, different values of 2 from the ones proposed are possible: in particular, setting 2 = 0 recovers the standard predictive control [18], in a similar way in which [2] is recovered as a special case of [19]. Furthermore, Lemma 1, does not pose constraints on the sign of 2 : for instance, choosing 2 = − 1 1 for = 1 also satisfies (27) as long as the remaining inequalities in Proposition 1 are verified.…”

“…Comparing the corresponding terms in (18) and (15) and simplifying the common factors results in the following inequalities:…”

“…The main challenges associated with this type of devices are the input delay due to the long supply lines, and the high friction forces. A simplified discrete-time model of a pneumatic cylinder based on the one proposed in [18] is:…”

“…The terms 1 , 2 , 3 in (38) represent the desired position, velocity and acceleration. It is straightforward to show that Assumptions 1-3 are satisfied for system (36): the sampling interval is constant for microcontrollers, while the input delay can be calculated knowing the length of the supply pipes; considering the bandwidth of the pneumatic drive (< 10 Hz) and the magnitude of the input delay (< 30 × 10 −3 seconds), the disturbances can be considered constant over the input delay; from [18], a suitable control law for the un-delayed version of system (36) with known friction coefficients ( = 0, 1 = 1 * , 2 = 2 * , 3 = 3 * ) that satisfies Assumption 3 is:…”