## 4 Simulation, Experiment, Analysis
### Training Results  
The DRL training in this paper was conducted on a computer with a Central Processing Unit (CPU) of Intel i7-9700k and a Graphics Processing Unit (GPU) of NVIDIA GeForce RTX 2080 Ti.  
The BCAMP model was trained by 2048 robots in parallel, and after 10,000 model iterations, the learning of actions from the motion trajectory library was accomplished. The weights of the reward functions involved in Section 3.3 are shown in Table 2, the hyperparameters involved in the training are shown in Table 3, and the mean reward is depicted in Figure 6. The mean reward value gradually increased and began to converge around 4000 iterations. The results indicate that the quadruped robot, trained with BCAMP, completed tasks well and received high rewards under different movement commands.  
To verify the training effectiveness, the trained BCAMP controller was applied in the simulation environment, and the movement of the quadruped robot was recorded, as shown in Figure 7. The policy was trained into a motion controller with various movement skills, allowing the robot to perform walking, running, jumping, and bipedal standing movements in the scene by issuing command parameters and user commands. It also enabled active switching between different stylistic actions.  
Figure 4: Optimized action joint position curves. (**a**) Optimized joint position curve for jumping action. (**b**) Joint position curve for bipedal standing action, where q1, q2,..., q7 represent the X and Z directions of the trunk’s position, the trunk’s pitch angle, and the joint angles of the front and rear thighs and calves, respectively. These curves depict the simplified overall state \(q(t)\) as it changes over time.  
Figure 5: Optimized action snapshots. (**a**) A snapshot of a simplified quadruped robot performing a jumping action. (**b**) A snapshot of a simplified quadruped robot bipedal standing on its rear foot.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Reward Function Parameters** & **Value** \\ \hline \(w^{s}\) & 0.35 \\ \(w\)s & 0.65 \\ \(r_{g}^{a}\) & 1 \\ \(r_{g}^{b}\) & 2 \\ \(r_{g}^{lin}\) & 2 \\ \(r_{ghg}^{lin}\) & 1.5 \\ \(r_{g}^{a}\) & 1 \\ \(\sigma\) & 0.25 \\ \(K_{P}\) & 100 \\ \(K_{3}\) & 0.98 \\ \(P\) & [0.2, 0.1] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Reward function weights.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Training Parameters** & **Value** \\ \hline Random initialization probability & 0.15 \\ Episode length (second) & 10 \\ Joint stiffness & 80 \\ Joint damping & 1 \\ Motor gain multiplier & [0.85, 1.15] \\ Friction between joints & [0.25, 1.75] \\ Added base mass & [\(-1,1\)] \\ Output action scaling probability & 0.75 \\ Control frequency & 33 Hz \\ Command resample time & 2 \\ PPO learning rate & 0.0005 \\ PPO discount factor & 0.998 \\ PPO clipping coefficient & 0.2 \\ Entropy regularization coefficient & 0.01 \\ Rate of increase in task reward weights & 0.3 \\ Discriminator loss factor & 1 \\ Discriminator regularization factor & 0.5 \\ Discriminator gradient penalty \(w^{sp}\) & 5 \\ Discriminator weight decay & 0.0001 \\ \hline \hline \end{tabular}
\end{table}
Table 3: BCAMP framework training hyperparameters.  
Figure 6: The mean reward evolves over the training iterations.  
In summary, the BCAMP successfully completed the training, and the trained controller effectively achieved active switching between walking, running, jumping, and bipedal standing actions, demonstrating the effectiveness of the BCAMP.