In this study, we propose the use of the phase-amplitude reduction method to construct an imitation learning framework. Imitating human movement trajectories is recognized as a promising strategy for generating a range of human-like robot movements. Unlike previous dynamical system-based imitation learning approaches, our proposed method allows the robot not only to imitate a limit cycle trajectory but also to replicate the transient movement from the initial or disturbed state to the limit cycle. Consequently, our method offers a safer imitation learning approach that avoids generating unpredictable motions immediately after disturbances or from a specified initial state. We first validated our proposed method by reconstructing a simple limit-cycle attractor. We then compared the proposed approach with a conventional method on a lemniscate trajectory tracking task with a simulated robot arm. Our findings confirm that our proposed method can more accurately generate transient movements to converge on a target periodic attractor compared to the previous standard approach. Subsequently, we applied our method to a real robot arm to imitate periodic human movements.

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit exponential convergence. LNO incorporates the pole-residue relationship between the input and the output space, enabling greater interpretability and improved generalization ability. Herein, we demonstrate the superior approximation accuracy of a single Laplace layer in LNO over four Fourier modules in FNO in approximating the solutions of three ODEs (Duffing oscillator, driven gravity pendulum, and Lorenz system) and three PDEs (Euler-Bernoulli beam, diffusion equation, and reaction-diffusion system). Notably, LNO outperforms FNO in capturing transient responses in undamped scenarios. For the linear Euler-Bernoulli beam and diffusion equation, LNO's exact representation of the pole-residue formulation yields significantly better results than FNO. For the nonlinear reaction-diffusion system, LNO's errors are smaller than those of FNO, demonstrating the effectiveness of using system poles and residues as network parameters for operator learning. Overall, our results suggest that LNO represents a promising new approach for learning neural operators that map functions between infinite-dimensional spaces.

In industrial process automation, sensors (pressure, temperature, etc.), controllers, and actuators (solenoid valves, electro-mechanical relays, circuit breakers, motors, etc.) make sure that production lines are working under the pre-defined conditions. When these systems malfunction or sometimes completely fail, alerts have to be generated in real-time to make sure not only production quality is not compromised but also safety of humans and equipment is assured. In this work, we describe the construction of a smart and real-time edge-based electronic product called PreMa, which is basically a sensor for monitoring the health of a Solenoid Valve (SV). PreMa is compact, low power, easy to install, and cost effective. It has data fidelity and measurement accuracy comparable to signals captured using high end equipment. The smart solenoid sensor runs TinyML, a compact version of TensorFlow (a.k.a. TFLite) machine learning framework. While fault detection inferencing is in-situ, model training uses mobile phones to accomplish the `on-device' training. Our product evaluation shows that the sensor is able to differentiate between the distinct types of faults. These faults include: (a) Spool stuck (b) Spring failure and (c) Under voltage. Furthermore, the product provides maintenance personnel, the remaining useful life (RUL) of the SV. The RUL provides assistance to decide valve replacement or otherwise. We perform an extensive evaluation on optimizing metrics related to performance of the entire system (i.e. embedded platform and the neural network model). The proposed implementation is such that, given any electro-mechanical actuator with similar transient response to that of the SV, the system is capable of condition monitoring, hence presenting a first of its kind generic infrastructure.

High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance control algorithms. We propose a design methodology that takes any given symmetry, linearises the associated error in a single set of coordinates, and uses LQR design to obtain a high performance control; an approach we term Equivariant Regulator design. We show that quadrotor vehicles admit several different symmetries: the direct product symmetry, the extended pose symmetry and the pose and velocity symmetry, and show that each symmetry can be used to define a global error. We compare the linearised systems via simulation and find that the extended pose and pose and velocity symmetries outperform the direct product symmetry in the presence of large disturbances. This suggests that choices of equivariant and group affine symmetries have improved linearisation error.