Environmental perception provides the necessary information for unmanned ground vehicles to recognize and interact with surrounding objects. Velodyne light detection and ranging (LiDAR) is widely used for this purpose due to its significant advantages such as high precision and being uninfluenced by varying illuminations. However, the unstructured distribution of LiDAR point clouds always affects the performance of feature extraction and object recognition. Moreover, the numbers of parameters in most deep learning models of object recognition are very large and the training process costs lots of computation consumption. This paper proposes a broad learning system (BLS) variant with a unified space autoencoder (USAE) as a lightweight model to recognize 3D objects. When the proposed method was evaluated on the LiDAR point cloud dataset and ModelNet10 dataset, the experimental results indicated that the recognition accuracy of our USAE-BLS model was similar to that of state-of-the-art 3D object recognition models. Moreover, the USAE-BLS has a much smaller model size and shorter training time than that of the deep learning models.