Sigma-point Kalman Filter with Nonlinear Unknown Input Estimation via Optimization and Data-driven Approach for Dynamic Systems

Most works on joint state and unknown input (UI) estimation require the assumption that the UIs are linear; this is potentially restrictive as it does not hold in many intelligent autonomous systems. To overcome this restriction and circumvent the need to linearize the system, we propose a derivative-free Unknown Input Sigma-point Kalman Filter (SPKF-nUI) where the SPKF is interconnected with a general nonlinear UI estimator that can be implemented via nonlinear optimization and data-driven approaches. The nonlinear UI estimator uses the posterior state estimate which is less susceptible to state prediction error. In addition, we introduce a joint sigma-point transformation scheme to incorporate both the state and UI uncertainties in the estimation of SPKF-nUI. An in-depth stochastic stability analysis proves that the proposed SPKF-nUI yields exponentially converging estimation error bounds under reasonable assumptions. Finally, two case studies are carried out on a simulation-based rigid robot and a physical soft robot, i.e., robots made of soft materials with complex dynamics to validate effectiveness of the proposed filter on nonlinear dynamic systems. Our results demonstrate that the proposed SPKF-nUI achieves the lowest state and UI estimation errors when compared to the existing nonlinear state-UI filters.

Cross-domain Transfer Learning and State Inference for Soft Robots via a Semi-supervised Sequential Variational Bayes Framework

Recently, data-driven models such as deep neural networks have shown to be promising tools for modelling and state inference in soft robots. However, voluminous amounts of data are necessary for deep models to perform effectively, which requires exhaustive and quality data collection, particularly of state labels. Consequently, obtaining labelled state data for soft robotic systems is challenged for various reasons, including difficulty in the sensorization of soft robots and the inconvenience of collecting data in unstructured environments. To address this challenge, in this paper, we propose a semi-supervised sequential variational Bayes (DSVB) framework for transfer learning and state inference in soft robots with missing state labels on certain robot configurations. Considering that soft robots may exhibit distinct dynamics under different robot configurations, a feature space transfer strategy is also incorporated to promote the adaptation of latent features across multiple configurations. Unlike existing transfer learning approaches, our proposed DSVB employs a recurrent neural network to model the nonlinear dynamics and temporal coherence in soft robot data. The proposed framework is validated on multiple setup configurations of a pneumatic-based soft robot finger. Experimental results on four transfer scenarios demonstrate that DSVB performs effective transfer learning and accurate state inference amidst missing state labels.