# Time Efficiency Improvement in Quadruped Walking with Supervised Training Joint Model
## 1 Introduction
Therefore, most studies that promote reinforcement learning for locomotion control will require choosing from a large controller family to develop a specific controller suitable to the task at hand. For example, [PERSON] et al. [11] created a dynamic motor model for a \"Minitaur\" quadruped robot that was used to learn the walking policy for locomotion control. In another study, [PERSON] et al. [12] proposed a hierarchical control approach for reinforcement learning to create a high-level and low-level control scheme for both the quadruped base and the overall locomotion control. Supervised learning-based models could be trained with a reliable dataset for locomotion. This eliminates the unpredictability of exploring and exploiting an action for locomotion during the training process, such as reinforcement learning. The supervised learning approach would be more efficient than reinforcement learning methods from the standpoint of computational efficiency during the learning process. With a reliable dataset, a joint model training using supervised learning could yield lower inaccuracies in the joint solution prediction, which could then lead to an optimized trained joint model suitable for autonomous walking scenarios. The benefits of a trained model could provide a one-off solution to support robotic control while maintaining time efficiency. By understanding the process of training models with supervised learning, the accuracy of a trained model could be pre-evaluated for reliability. Reliable control accuracy and time-efficiency in quadruped locomotion control have provided the motivation for this study. Although [PERSON] et.al identified the benefits of supervised learning implementation in robotics, a training method for a high degree-of-freedom robot remains unsolved [13]. Therefore, we focused on training the individual joints model of the quadruped and then combining them to perform a walk. Therefore, this study proposed an offline approach for building a simplified locomotion control policy using a supervised learning method for a 12-degree-of-freedom quadruped robot. The joint solution generated from the conventional method proposed by [PERSON] et al. [10] was used, which has been proven capable of performing stable quadruped walk motions and whose sample data were, therefore, suitable for generating a joint model using a supervised learning algorithm. Therefore, the dataset used in this study originated from the stable walking control algorithm proposed by [PERSON] et al. After obtaining the joint model through the application of a supervised learning algorithm, the robot's leg joints were trained to predict the joint solution for a walking sequence. Furthermore, the data features from the previous study's dataset included the robot states (robot position before and after each single-cycle walking motion) and the respective sequence of joint solutions. Each walking sequence involved the analysis of multi-input and multi-output data features for joint model training. Among the training methods available for supervised learning, the multilayer perceptron algorithm was ideal for implementing multi-input-multi-output (MIMO) training. Therefore, the multilayer perceptron method was implemented in this study. The trained models were compared with a test set (see Section 6.1) and were subsequently evaluated using a 3D quadruped robot in the GAZEBO simulation environment (see Section 6.2). The remainder of this paper is organized as follows. The robot configuration is described in Section 2. The concept of ZMP is described in Section 3. The data generation method is explained in Section 4. An overview of the control policy is presented in Section 5. The evaluation results of the proposed control policy are presented in Section 6.