Quadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton–Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin’s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.

The primary goal was to investigate the effects of l-carnitine on fuel efficiency, as an antioxidant, and for muscle recovery in Labrador retrievers. Dogs were split into two groups, with one group being supplemented with 250 mg/d of Carniking™ l-carnitine powder. Two experiments (Expt 1 and Expt 2) were performed over a 2-year period which included running programmes, activity monitoring, body composition scans and evaluation of recovery using biomarkers. Each experiment differed slightly in dog number and design: fifty-six v. forty dogs; one endurance and two sprint runs per week v. two endurance runs; and differing blood collection time points. All dogs were fed a low-carnitine diet in which a fixed amount was offered based on maintaining the minimum starting weight. Results from Expt 1 found that the carnitine dogs produced approximately 4000 more activity points per km compared with the control group during sprint (P = 0·052) and endurance runs (P = 0·0001). Male carnitine dogs produced half the creatine phosphokinase (CPK) following exercise compared with male control dogs (P = 0·05). Carnitine dogs had lower myoglobin at 6·69 ng/ml following intensive exercise compared with controls at 24·02 ng/ml (P = 0·0295). Total antioxidant capacity (TAC) and thiobarbituric acid reactive substance (TBARS) results were not considered significant. In Expt 2, body composition scans indicated that the carnitine group gained more total tissue mass while controls lost tissue mass (P = 0·0006) and also gained lean mass while the control group lost lean mass (P < 0·0001). Carnitine dogs had lower CPK secretion at 23·06 v. control at 28·37 mU/ml 24 h after post-run (P = 0·003). Myoglobin levels were lower in carnitine v. control dogs both 1 h post-run (P = 0·0157; 23·83 v. 37·91 ng/ml) and 24 h post-run (P = 0·0189; 6·25 v.13·5 ng/ml). TAC indicated more antioxidant activity in carnitine dogs at 0·16 mmv. control at 0·13 mm (P = 0·0496). TBARS were also significantly lower in carnitine dogs both pre-run (P = 0·0013; 15·36 v. 23·42 µm) and 1 h post-run (P = 0·056; 16·45 v. 20·65 µm). Supplementing l-carnitine in the form of Carniking™ had positive benefits in Labrador retrievers for activity intensity, body composition, muscle recovery and oxidative capacity.

The purpose of this study is to determine the navigation efficiency for transiting from various ports in Asia and Rotterdam in Europe via the Northern Sea Route. Navigation efficiency was derived from fuel consumption ratios. Preliminary research results showed that fuel consumption and the amount of carbon dioxide emissions was reduced by transiting from various ports through the European Sea Route, and the navigation efficiencies of the various ports ranked in the following descending order: Yokohama - Busan - Shanghai - Kaohsiung - Hong Kong - Singapore. The higher the ratio was, the lower the navigation efficiency of using the Northern Sea Route, i.e. more fuel was consumed and travel costs were higher. In contrast, the lower the ratio was, the higher the navigation efficiency, i.e. less fuel was consumed and travel costs were lower. Recommendations were discussed in the study.