This paper addresses the finite-time stabilization problem for a nonholonomic wheeled mobile robot (NWMR) with input constraints. By utilizing the hyperbolic tangent function tanh(·), bounded finite-time stabilization controllers are developed. In addition, an explicit upper-bound estimate for the closed-loop settling time is given, and the level of input constraints is characterized by parameters that depend on the actuator’s capacity. A thorough finite-time stability analysis is carried out using appropriate Lyapunov functions. For a compact set contained in the domain of attraction, a guideline is presented to clarify how to construct it. Finally, simulation results show the effectiveness of the developed controllers.
The behaviour of co-axial rotors is well understood, and they are especially practical for large UAVs due to their increased thrust without changing the vehicle footprint. However, for co-axial systems with varying propeller diameters between the two disks, research is more limited. The goal of this paper was to determine an optimal configuration for several different unequal co-axial setups using numerous different propeller combinations and separation ratios. Propellers with diameters of 26 and 29 inches are tested at separation ratios of 0.05 to 0.35. Thrust and power were collected using an off-the-shelf FS15-TYTO thrust stand, with the upstream and downstream propellers running at equal throttles. From this, performance was assessed through efficiency, thrust, and power consumption, and comparisons were made to an ideal combination without losses. The results show that for unequal combinations, the user should place the smaller propeller upstream for greater efficiency, but for maximum thrust capacity, two equal propellers are preferred. When compared to two independent rotors of the same size, a 26″ upstream rotor and a 29″ downstream rotor minimised thrust loss to 16%, compared to 23% for the opposite arrangement. It was also found that the optimal separation ratio is always approximately 0.2.
