The search efficiency of a rapidly exploring random tree (RRT) can be improved by introducing a high-probability goal bias strategy. In the case of multiple complex obstacles, the high-probability goal bias strategy with a fixed step size will fall into a local optimum, which reduces search efficiency. Herein, a bidirectional potential field probabilistic step size rapidly exploring random tree (BPFPS-RRT) was proposed for the path planning of a dual manipulator by introducing a search strategy of a step size with a target angle and random value. The artificial potential field method was introduced, combining the search features with the bidirectional goal bias and the concept of greedy path optimization. According to simulations, taking the main manipulator as an example, compared with goal bias RRT, variable step size RRT, and goal bias bidirectional RRT, the proposed algorithm reduces the search time by 23.53%, 15.45%, and 43.78% and decreases the path length by 19.35%, 18.83%, and 21.38%, respectively. Moreover, taking the slave manipulator as another example, the proposed algorithm reduces the search time by 6.71%, 1.49%, and 46.88% and decreases the path length by 19.88%, 19.39%, and 20.83%, respectively. The proposed algorithm can be adopted to effectively achieve path planning for the dual manipulator.

The operating point of a propeller hydropower station will deviate from the effective workspace while the discharge reduces excessively during dry seasons. It usually leads to a decrease in efficiency and even to being unable to work. To solve the above problem, a scheme named decreasing capacity to increase efficiency was presented in this article. A low-specific-speed propeller runner with fixed blades that has the same installing dimensions as the original one was redesigned and equipped in dry seasons. A positive circulation at the outlet of the blades bigger than in conventional runners is allowed. Some key technologies about hydraulic design for runner blades were researched, which include distribution of velocity circulation at the inlet and outlet of the runner, thickening of the epiphyseal line of an aerofoil, unfolding aerofoil being converted to a cylindrical section, etc. In the section on digital modeling for runner blades, aerofoils on the cylindrical sections at the rim and at the hub were constructed employing the trend extrapolation method. Moreover, a blade digital model was built at one time according to the aerofoils on all cylindrical sections by means of a successful redevelopment to UniGraphics, and it has perfect symmetry. A case presented indicates that the method of decreasing capacity to increase efficiency is feasible. Using the method, the turbine efficiency increased from less than 28.6% to 83.4% while the discharge decreased from 3.20 m³s⁻¹ to 1.00 m³s⁻¹, and then the hydropower unit was able to work properly.