Stochastic LPV MPC-based path following control for bevel-tip flexible needle with probabilistic constraints

Abstract This paper addresses the path-tracking problem for flexible needle control systems using a stochastic linear parameter varying (LPV) and model predictive control (MPC) strategy. Flexible needles operating in dynamic environments with non-uniform tissue density often deviate from ideal assumptions, resulting in non-standard models. The bicycle kinematics model for flexible needle motion control is transformed into an LPV model, improving accuracy and enabling more efficient control. The proposed stochastic LPV MPC approach aims to mitigate uncertainties arising from modelling errors and dynamic environmental factors, ensuring accurate trajectory tracking for the flexible needle. The sample and removal method is utilized to reformulate the probabilistic-constrained optimization problem for implementation. The contributions of this work lie in the application of stochastic LPV MPC to address the trajectory tracking problem in the presence of uncertainties. The simulation results illustrate the superior robustness of the stochastic LPV MPC approach, as evidenced by significantly smaller tracking errors across various scenarios.