This article applies novel results for infinite- and finite-horizon optimal control problems with nonlinear dynamics and constraints. We use the Valentine transformation to convert a constrained optimal control problem into an unconstrained one and show uniqueness of the value function to the corresponding Hamilton–Jacobi–Bellman (HJB) equation. From there, we show how to approximate the solution of the initial (in)finite-horizon problem with a family of solutions that is $$\varGamma $$Γ -convergent. Optimal solutions are efficiently obtained via a solver based on Pontryagin’s Principle (PP). The proposed methodology is demonstrated on the path planning problem using the full nonlinear dynamics of an unmanned aerial vehicle (UAV) and autonomous underwater vehicle (AUV) involving state constraints in 3D environments with obstacles.

In this article we consider the problem of tether entanglement for tethered mobile robots. One of the main risks of using a tethered connection between a mobile robot and an anchor point is that the tether may get entangled with the obstacles present in the environment or with itself. To avoid these situations, a non-entanglement constraint can be considered in the motion planning problem for tethered robots. This constraint is typically expressed as a set of specific tether configurations that must be avoided. However, the literature lacks a generally accepted definition of entanglement, with existing definitions being limited and partial in the sense that they only focus on specific instances of entanglement. In practice, this means that the existing definitions do not effectively cover all instances of tether entanglement. Our goal in this article is to bridge this gap and to provide new definitions of entanglement, which, together with the existing ones, can be effectively used to qualify the entanglement state of a tethered robot in diverse situations. The new definitions find application in motion planning for tethered robots, where they can be used to obtain more safe and robust entanglement-free trajectories.

The aim of this paper is to investigate the possibility of drone optimization by selecting and testing the best material suitable for additive manufacturing technology and generative design approach, i. e. shape optimization. The use of additive manufacturing technology enables the creation of models of more complex shapes that are difficult or impossible to produce with conventional processing methods. The complex and unconventional design of the drone body can open up many possibilities for weight reduction while maintaining the strength of the drone body. By using 3D printing in addition to FEM (Finite Element Method) analysis, and generative design it can identify areas of the drone body that are overdrawn, allowing it to either lift off material or simply change the design at these areas. Choosing the right material for this application is crucial in order to optimise the mechanical properties of the material with weight, material cost, printability and availability of the material and the 3D printing method, while at the same time reducing environmental pollution. The goal is to reduce the drone mass by 15–20 % using generative design tools. Mass is an important segment when prototyping a drone. If the drone is too heavy, more lift power is needed to keep the drone in the air, so the propellers have to turn faster and use more energy. Consequently, the reduction of drone mass should increase the take-off weight. In this article 5 commercial drones of similar characteristics are compared with the final proposal of our 3D printed drone (Prototype 1). The rotor distance between the drones, the weight of the electric motor and the take-off weight are compared. The goal was to produce a prototype with a big rotor distance-to-weight ratio, and take-off weight bigger than observed drones have. The defined goal function was optimized in order to evaluate characteristics of 12 different 3D printed materials. Following properties: ultimate strength, stiffness, durability, printability of the material, and required bed and extruder temperature for printing were taken in consideration to select optimal material. Polycarbonate proved to be the best choice for 3D printing UAVs

Here, agents learn how often to exchange information with neighbours in cooperative multi‐agent systems (MASs) such that their linear quadratic regulator (LQR)‐like performance indices are minimized. The investigated LQR‐like cost functions capture trade‐offs between the energy consumption of each agent and MAS local control performance in the presence of exogenous disturbances, delayed and noisy data. Agent energy consumption is critical for prolonging the MAS mission and is composed of both control (e.g. acceleration, velocity) and communication efforts. Taking provably stabilizing upper bounds on broadcasting intervals as optimization constraints, an online off‐policy model‐free learning algorithm based on least square policy iteration (LSPI) to minimize the cost function of each agent is employed. Consequently, the obtained broadcasting intervals adapt to the most recent information (e.g. delayed and noisy agents' inputs and/or outputs) received from neighbours whilst provably stabilize the MAS. Chebyshev polynomials are utilized as the approximator in the LSPI whereas Kalman filtering handles sampled, corrupted, and delayed data. Subsequently, convergence and near‐optimality of our LSPI scheme are inspected. The proposed methodology is verified experimentally using an inexpensive motion capture system and nano quadrotors.