We propose a novel approach to track the state of charge (SoC) of batteries in mobile robots to improve their capabilities. The batteries' status is critical to accomplish their mission, but limited battery life can be a challenge. Our methodology focuses on modeling and estimating the SoC of batteries through system identification and fractional-order models. These models are flexible and can adjust to transient responses, allowing for accurate estimation of battery characteristics. Specifically, we use cubic spline interpolation to obtain the open-circuit voltage (OCV) and the different resistors of the battery model. To estimate the SoC, we deploy a novel approach based on the moving horizon estimation (MHE) algorithm, which is suitable for handling poor initial estimation and constraints on the battery model. We consider the constraint on the peak discharging current, which can limit the performance of mobile robots in low-battery mode. We validate our approach by applying system identification and MHE to data from a mobile robot. The results show that our method accurately estimates the SoC despite poor initial values, enabling improved performance for mobile robots.

Objective. Bi-directional electronic neural interfaces, capable of both electrical recording and stimulation, communicate with the nervous system to permit precise calibration of electrical inputs by capturing the evoked neural responses. However, one significant challenge is that stimulation artifacts often mask the actual neural signals. To address this issue, we introduce a novel approach that employs dynamical control systems to detect and decipher electrically evoked neural activity despite the presence of electrical artifacts. Approach. Our proposed method leverages the unique spatiotemporal patterns of neural activity and electrical artifacts to distinguish and identify individual neural spikes. We designed distinctive dynamical models for both the stimulation artifact and each neuron observed during spontaneous neural activity. We can estimate which neurons were active by analyzing the recorded voltage responses across multiple electrodes post-stimulation. This technique also allows us to exclude signals from electrodes heavily affected by stimulation artifacts, such as the stimulating electrode itself, yet still accurately differentiate between evoked spikes and electrical artifacts. Main results. We applied our method to high-density multi-electrode recordings from the primate retina in an ex vivo setup, using a grid of 512 electrodes. Through repeated electrical stimulations at varying amplitudes, we were able to construct activation curves for each neuron. The curves obtained with our method closely resembled those derived from manual spike sorting. Additionally, the stimulation thresholds we estimated strongly agreed with those determined through manual analysis, demonstrating high reliability ( R 2 = 0.951 for human 1 and R 2 = 0.944 for human 2). Significance. Our method can effectively separate evoked neural spikes from stimulation artifacts by exploiting the distinct spatiotemporal propagation patterns captured by a dense, large-scale multi-electrode array. This technique holds promise for future applications in real-time closed-loop stimulation systems and for managing multi-channel stimulation strategies.