Design and comparison of trajectory tracking controllers for a hybrid surgical robot employing PID, sliding Mode and RBFNN-based adaptive Control strategies

Minimally invasive surgery (MIS) requires sub-millimeter accuracy and smooth trajectory of instruments, but hybrid surgical robots (HSRs) have configuration-dependent nonlinear coupled dynamics that adversely affect tracking dynamics and add oscillatory behavior. Despite increasing interest in hybrid surgical architectures, very limited studies objectively measure the tradeoffs between classical, robust, and adaptive controllers within the same HSR. Based on this, this manuscript presents detailed modeling and simulation of an eight-degree-of-freedom HSR, consisting of a parallel positioning platform, and a serial manipulator, and compares three trajectory-tracking methods namely (i) conventional PID controller, (ii) boundary-layer based sliding-mode controller (SMC), and (iii) Radial Basis Function Neural Network (RBFNN) based adaptive PID controller. For a common 3D trajectory, PID controller has the greatest transient errors with maximum deviations of 2 mm for parallel platform and 2.5 mm for serial manipulator and sluggish convergence in 32–40s. SMC controller minimizes peak errors to 0.85–1.05 mm (parallel platform) and 1.10–1.25 mm (serial module), achieves faster convergence in 20–23s, but exhibits a chattering index of 0.42. The RBFNN-adaptive PID controller offers the best tradeoff by reducing the error peaks to 0.46–0.65 mm (parallel platform) and 0.78–0.82 mm (serial module), cut the mean actuator force by half to 0.56 N, and reached the smoother control action in 19–22s with significantly reduced oscillations. These results indicate that the online gain adaptation approach can be used to make HSR trajectory tracking more accurate and less oscillatory in coupled nonlinear dynamics and thus promotes safer and more precise MIS motion control.