Planar fiducial markers are commonly used to estimate a pose of a camera relative to the marker. This information can be combined with other sensor data to provide a global or local position estimate of the system in the environment using a state estimator such as the Kalman filter. To achieve accurate estimates, the observation noise covariance matrix must be properly configured to reflect the sensor output’s characteristics. However, the observation noise of the pose obtained from planar fiducial markers varies across the measurement range and this fact needs to be taken into account during the sensor fusion to provide a reliable estimate. In this work, we present experimental measurements of the fiducial markers in real and simulation scenarios for 2D pose estimation. Based on these measurements, we propose analytical functions that approximate the variances of pose estimates. We demonstrate the effectiveness of our approach in a 2D robot localisation experiment, where we present a method for estimating covariance model parameters based on user measurements and a technique for fusing pose estimates from multiple markers.

We study two nilpotent affine control systems derived from the dynamic and control of a vertical rolling disc that is a simplification of a differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated and optimal control problems are formulated, and their Hamiltonian systems of ODEs are derived using the Pontryagin maximum principle. These optimal control problems completely determine the energetically optimal trajectories between two states. Then, a novel numerical algorithm based on optimisation for finding the Maxwell points is presented and tested on these control systems. The results show that the use of such numerical methods can be beneficial in cases where common analytical approaches fail or are impractical.

Energy harvesting is an important topic today. Complex monitoring systems with many nodes need energy sources and vibration energy harvesters (VEHs) could be one type of them. Mathematical model of the VEH is necessary instrument to estimate possible harvested power. This paper deals with piezoelectric VEH in setting as cantilever beam with tip mass. Traditional linear model of this type of VEH is simple, however, it represents the VEH only in one operating point and in another one (another amplitude of excitation vibrations) it could return wrong results. The nonlinear model of VEH is introduced in this paper with its parameters estimation. The nonlinear model is compared with linear model and experiment to demonstrate difference between them in amplitude frequency characteristics. Finally, the average harvested power from harmonic vibrations is measured experimentally and compared with prediction from linear and nonlinear model.

Reinforcement learning (RL) agents can learn to control a nonlinear system without using a model of the system. However, having a model brings benefits, mainly in terms of a reduced number of unsuccessful trials before achieving acceptable control performance. Several modelling approaches have been used in the RL domain, such as neural networks, local linear regression, or Gaussian processes. In this article, we focus on techniques that have not been used much so far: symbolic regression (SR), based on genetic programming and local modelling. Using measured data, symbolic regression yields a nonlinear, continuous‐time analytic model. We benchmark two state‐of‐the‐art methods, SNGP (single‐node genetic programming) and MGGP (multigene genetic programming), against a standard incremental local regression method called RFWR (receptive field weighted regression). We have introduced modifications to the RFWR algorithm to better suit the low‐dimensional continuous‐time systems we are mostly dealing with. The benchmark is a nonlinear, dynamic magnetic manipulation system. The results show that using the RL framework and a suitable approximation method, it is possible to design a stable controller of such a complex system without the necessity of any haphazard learning. While all of the approximation methods were successful, MGGP achieved the best results at the cost of higher computational complexity. Index Terms–AI‐based methods, local linear regression, nonlinear systems, magnetic manipulation, model learning for control, optimal control, reinforcement learning, symbolic regression.

This paper deals with vibration energy harvesting tests and measurements in lab conditions and subsequent redesign of tunable parameters. The presented device generates electrical energy from ambient mechanical vibrations, which occur in potential engineering applications. This device could be used for autonomous powering of wireless sensors with the average power consumption in the range of several mW. The presented device harvests maximal electrical power in resonance operation, which is tuned by the seismic mass and the stiffness ratio. The stiffness element, which is based on the magnetic force of repelling rare earth magnets, is used for tuning up of the resonance operation. The linear system harvests electrical energy only in narrow bandwidth of the tuned frequency. The ways of improving the amount of harvested electrical energy in wider frequency range are observed during nonlinear operation. The corrected harvesting system positioning in the principal direction of the excitation acceleration and the nonlinear redesign of the energy harvesting system with extended frequency bandwidth are presented in this paper.