Incremental Heteroscedastic Gaussian Process Regression and Its Applications in Model Predictive Control

Gaussian process regression (GPR) models are becoming increasingly tightly integrated into robotic systems, particularly in the context of robot model predictive control (MPC) operating in complex environments. Because data generated by robots are typically collected online and exhibits heteroscedasticity (i.e., the noise variance depends on the input), traditional GPR may not be suitable. Thus, an incremental heteroscedastic GPR (IHGPR) method is proposed, which takes advantage of incremental sparse spectrum GPR (I-SSGPR) and the framework of improved most likely heteroscedastic GPR (improved MLHGPR). The predictive distribution is not only in an explicit form but also differentiable, rendering a plug-and-play solution for optimization-based control. The efficacy of the proposed approach is demonstrated through a series of empirical evaluation experiments, highlighting its time efficiency and capacity to accurately capture heteroscedastic signals. To illustrate its versatile applicability in robotic system control, we integrate IHGPR into a robust MPC (RMPC) method to online fit the state-and input-dependent heteroscedastic stochastic disturbances and present the applicability and efficiency through simulation results.