In view of such flaws as poor map exploration ability, large and discontinuous turning angles, and inability to meet the kinematic model found in quadruped robots using the RRT (rapidly-exploring random tree) algorithm for path planning, an RRT path planning algorithm has thus been proposed with a combination of the constraints of the quadruped robot’s own model. With the kinematic constraints and volume of quadruped robots taken into consideration, an optimization can be achieved of the turning point by using local Bessel curve transformation. The search efficiency of the algorithm can be improved by utilizing global adaptive step size, node self updating, and increasing target bias. The simulation experiment results of quadruped robots show that the improved RRT algorithm generates paths with strong feasibility and high operational efficiency, meeting the requirements of quadruped robots for paths in practical engineering, thus significantly reducing the time to reach the destination.