Improving Haptic Transparency for Uncertain Virtual Environments Using Adaptive Control and Gain-Scheduled Prediction

The realism or transparency of haptic interfaces is becoming more critical as they are applied to training in fields like minimally invasive surgery (MIS). Surgical training simulators must provide a transparent virtual environment (VE) at a high update rate. Complex, deformable, cuttable tissue models have nonlinear dynamics and are computationally expensive, making it difficult to provide sufficient update rates. The objective of this work is to improve the transparency for this type of VE by formulating the unknown nonlinear dynamics as a quasi-linear parameter varying (LPV) system and designing a predictor to provide an output at a much higher update rate. An adaptive controller based on gain-scheduled prediction is considered for a nonlinear haptic device and a nonlinear, delayed, and sampled VE. The predictor uses feedback from the more accurate but slow-updating VE to update a simplified dynamic model. The predictor is designed based on numerical solutions to a linear matrix inequality derived using Lyapunov-based methods. Experimental results demonstrate the effectiveness of the gain-scheduled predictor approach and compare it to previous work using a constant-gain predictor. The gain-scheduled predictor results in significant performance improvements compared to a haptic system without prediction, but less significant improvement compared to the constant-gain approach.