Aiming at the problems of difficult weeding operation, low weeding efficiency and low level of intelligence in orchards in hilly and mountainous areas, a small mountain orchard weeding robot was designed. In order to improve the tracking accuracy of the tracked weeding robot's operation path, the research of tracked weeding robot's path tracking control algorithm was carried out. The ‘inverted triangle swivel structure’ was used to design an imitation floating chassis, which carried a ‘Y-type’ blade assembly for crushing and weeding and powered by an extended-range hybrid power system, and a slope steering control strategy based on model predictive control was proposed to address the problem of large slope steering slippage. The round-trip path planning method was used to plan the full coverage path of the orchard. Combined with BDS positioning and navigation technology and full coverage path planning, the crawler weeding robot was ensured to have high tracking accuracy during operation. The kinematic model of the crawler weeding robot was constructed, and the steering dynamics and control strategy of the crawler weeding robot on the slope were simulated and analyzed in MATLAB software. The simulation results show that the average error of the designed slope steering model is only 0.039 m under the condition of 15°, which demonstrates a good accuracy. Field experiments show that the MPC controller proposed in this paper can effectively improve the path tracking effect under slope steering conditions, and the average error under uphill and downhill conditions is reduced by 51.76% and 63.77%, respectively, compared with the PID controller when the slope angle is 15°. The weeding robot integrated with BeiDou navigation function has an effective weeding rate higher than 97% and can walk normally on a 25° slope. The research results provide a reference for the development of weeding robots in hilly and mountainous areas.