A from-scratch implementation of Proximal Policy Optimization (PPO) for training a quadruped ant robot in MuJoCo's Ant-v5 environment. Features include height stability penalty to prevent hopping behavior, parallel environment training, and comprehensive visualization tools.
Full quality video
[demo_2x2.mp4](https://github.com/mturan33/mujoco-ant-ppo/releases/download/v1.0/demo_2x2.mp4)Four trained models running simultaneously: Vanilla BEST (2739), Anti-Hopping (2531), Learning Phase (1828), and Energy Efficient (1261)
- PPO from Scratch: Complete implementation without high-level RL libraries
- Height Stability Penalty: Novel reward shaping to discourage hopping behavior
- Parallel Training: 16 parallel environments for 5x faster training
- Observation Normalization: Running mean/std for stable learning
- Comprehensive Visualization: TensorBoard logging + 2x2 grid demo
- Deterministic Results: Seed control and reproducible training
What is PPO?
Instead of directly maximizing the true objective (total cumulative reward), PPO optimizes a surrogate objective function. This surrogate is then clipped to prevent excessively large and dangerous policy updates, ensuring stable and monotonic improvement.
Key Innovation:
The clipped surrogate objective constrains the ratio between new and old policies within [1-ε, 1+ε], where ε is typically 0.2. This prevents the policy from changing too drastically in a single update, avoiding performance collapse.
Mathematical Formulation:
L^CLIP(θ) = E_t [ min(r_t(θ)·Â_t, clip(r_t(θ), 1-ε, 1+ε)·Â_t) ]
where:
- r_t(θ) = π_θ(a_t|s_t) / π_θ_old(a_t|s_t) (probability ratio)
- Â_t = advantage estimate (GAE)
- ε = clip ratio (0.2)
| Approach | Avg Reward | Training Time | Stability | Speed (steps/s) |
|---|---|---|---|---|
| Anti-Hopping | 2531 | 5.1h | Smooth | 10,200 |
| Vanilla BEST | 2473 | 5.5h | Hopping | 9,500 |
| Learning Phase | 1828 | 11.9h | Learning | 8,300 |
| Energy Efficient | 1261 | 1.5h | Stable | 10,800 |
Training hardware: NVIDIA RTX 5070 Ti (12GB VRAM)
Observations:
- Anti-Hopping (blue) achieves stable convergence around 6M steps
- Vanilla (cyan) shows higher variance due to hopping behavior
- Energy Efficient (green/orange) converges quickly but plateaus at lower reward
Actor-Critic Dynamics:
- Actor loss stabilizes around 0.02 after initial exploration
- Critic loss decreases from ~5000 to ~500, indicating improved value estimation
- Both networks converge without catastrophic divergence
Exploration Schedule:
- Action standard deviation starts at 1.0 for broad exploration
- Decays to ~0.25 by 8M steps for exploitation
- Energy Efficient model maintains slightly higher std for robustness
Performance Metrics:
- Average speed: 9,500-10,800 steps/second
- Parallel environments (16x) provide significant speedup
- Occasional spikes due to checkpoint saving
| Parameter | Value | Description |
|---|---|---|
| Actor Learning Rate | 3e-4 | Adam optimizer for policy network |
| Critic Learning Rate | 3e-4 | Adam optimizer for value network |
| Discount Factor (γ) | 0.99 | Future reward discount |
| GAE Lambda (λ) | 0.95 | Advantage estimation smoothing |
| Clip Ratio (ε) | 0.2 | PPO clipping parameter |
| Rollout Steps | 512 | Steps per environment per update |
| Update Epochs | 10 | Optimization epochs per batch |
| Batch Size | 64 | Mini-batch size for SGD |
| Entropy Coefficient | 0.01 | Exploration bonus weight |
| Parallel Environments | 16 | Simultaneous training instances |
Actor (Policy Network):
Input (27) → FC(256) → Tanh → FC(256) → Tanh → FC(128) → Tanh → FC(8) → Tanh
↓
Action Mean + Log Std
Critic (Value Network):
Input (27) → FC(256) → Tanh → FC(256) → Tanh → FC(128) → Tanh → FC(1)
↓
State Value
Key Features:
- Orthogonal weight initialization (gain = √2)
- Tanh activations for bounded outputs
- Separate actor-critic architecture (not shared)
- Diagonal Gaussian policy with learned log std
normalized_obs = (obs - running_mean) / sqrt(running_var + 1e-8)
clipped_obs = clip(normalized_obs, -10, 10)- Running statistics updated via Welford's online algorithm
- Prevents gradient explosion from large observation values
- Critical for stable training in continuous control
δ_t = r_t + γ·V(s_{t+1}) - V(s_t)
A_t = Σ_{l=0}^∞ (γλ)^l · δ_{t+l}- Balances bias-variance trade-off (λ = 0.95)
- Reduces variance compared to Monte Carlo returns
- Enables multi-step bootstrapping
torch.nn.utils.clip_grad_norm_(parameters, max_norm=0.5)- Prevents exploding gradients
- Stabilizes training in complex environments
lr(t) = lr_0 · max(0.5, 1 - t/T)- Linear decay to 50% of initial learning rate
- Improves final convergence quality
Observation:
Standard PPO on Ant-v5 learns to "hop" rather than walk smoothly. While this achieves high rewards (~2473), it exhibits:
- Excessive vertical movement (height variance > 0.1)
- Unstable gait patterns
- Unrealistic locomotion for real-world deployment
Root Cause:
The default Ant-v5 reward function:
reward = forward_velocity - 0.5 * control_cost - 0.0005 * contact_costdoesn't penalize vertical instability. The agent exploits this by hopping to maximize forward velocity.
Our Solution: Height Stability Penalty
height_variance = abs(current_height - previous_height)
stability_penalty = -8.0 * height_variance
shaped_reward = base_reward + stability_penaltyResults:
- Maintained 102% of baseline performance (2531 vs 2473)
- Reduced height variance by 85%
Comparison:
| Metric | Vanilla | Anti-Hopping | Change |
|---|---|---|---|
| Avg Reward | 2473 | 2531 | +2.3% |
| Height Variance | 0.089 | 0.013 | -85% |
| Forward Speed | 2.8 m/s | 2.7 m/s | -3.6% |
- Python 3.8+
- CUDA-capable GPU (recommended)
- 8GB+ RAM
# Clone repository
git clone https://github.com/mturan33/mujoco-ant-ppo.git
cd mujoco-ant-ppo
# Create virtual environment
python -m venv venv
source venv/bin/activate # On Windows: venv\Scripts\activate
# Install dependencies
pip install -r requirements.txtgymnasium==0.29.1
torch==2.0.1
numpy==1.24.3
mujoco==3.0.0
opencv-python==4.8.0.74
matplotlib==3.7.1
tensorboard==2.13.0
stable-baselines3==2.1.0Note: Install PyTorch with appropriate CUDA version from pytorch.org
# Train
python main_parallel.py
# Expected output:
# [INFO] Creating 16 parallel environments...
# [INFO] Height Stability Penalty: 8.0
# [START] Training with Height Stability Penalty
# [EPISODE 1] Step: 512 | Reward: 1234.56 | Avg-100: 0.00 | Speed: 10200 steps/sTraining Configuration:
- Total timesteps: 8,000,000
- Parallel environments: 16
- Expected time: ~30 minutes (RTX 5070 Ti)
- Expected final reward: ~2500
# Test trained agent with visualization
python test_agent.py
# Output:
# [DEVICE] Using: cuda
# [OK] Loaded model: Ant-v5_PPO_ANTIHOPPING_16envs_2025-11-05_18-09-09_BEST
# [START] Testing for 10 episodes
# [EPISODE 1/10] Reward: 2534.21 | Steps: 1000
# ...
# [RESULTS] Average Reward: 2531.23# 2x2 grid demo (compare 4 models side-by-side)
python demo_2x2.py
# Controls:
# - 'q' or ESC: Quit
# - 's': Save screenshot
# Output: demo_2x2_YYYYMMDD_HHMMSS.mp4
# Export TensorBoard plots as PNG
python export_tensorboard_plots.py
# View live training progress
tensorboard --logdir=./runs --port=6006
# Navigate to: http://localhost:6006mujoco-ant-ppo/
├── README.md # This file
├── requirements.txt # Python dependencies
├── .gitignore # Git ignore rules
├── LICENSE # MIT License
│
├── ppo_agent.py # Core PPO implementation
├── main_parallel.py # Training script (height stability)
├── test_agent.py # Evaluation script
├── demo_2x2.py # 2x2 visual comparison
├── select_models.py # Model selection utility
├── export_tensorboard_plots.py # Plot generation
│
├── assets/ # Images for README
│ ├── demo_2x2.mp4 # Demo video
│ ├── training_rewards.png # Learning curves
│ ├── final_comparison.png # Performance comparison
│ ├── loss_curves.png # Actor-critic losses
│ ├── exploration_std.png # Exploration decay
│ └── training_speed.png # Training efficiency
│
├── models/ # Trained models (gitignored)
│ └── .gitkeep
│
└── runs/ # TensorBoard logs (gitignored)
└── .gitkeep
from ppo_agent import PPOAgent
import gymnasium as gym
# Create environment
env = gym.make('Ant-v5')
# Initialize agent
agent = PPOAgent(
state_dim=27,
action_dim=8,
max_action=1.0,
actor_lr=3e-4,
critic_lr=3e-4,
gamma=0.99,
gae_lambda=0.95,
clip_ratio=0.2,
device='cuda'
)
# Training loop
state = env.reset()[0]
for step in range(1_000_000):
action, log_prob, value = agent.get_action(state)
next_state, reward, done, truncated, info = env.step(action)
# Apply height stability penalty
height_variance = abs(next_state[0] - state[0])
shaped_reward = reward - 8.0 * height_variance
# Store transition and learn...
state = next_state if not (done or truncated) else env.reset()[0]import torch
from ppo_agent import PPOAgent
# Load trained model
agent = PPOAgent(state_dim=27, action_dim=8, max_action=1.0, ...)
agent.load("models", "Ant-v5_PPO_ANTIHOPPING_16envs_BEST")
# Deterministic evaluation
state = env.reset()[0]
total_reward = 0
for _ in range(1000):
with torch.no_grad():
state_tensor = torch.FloatTensor(state).unsqueeze(0)
norm_state = (state_tensor - agent.obs_rms.mean) / torch.sqrt(agent.obs_rms.var + 1e-8)
action_dist = agent.actor(norm_state)
action = action_dist.mean # Deterministic (no sampling)
state, reward, done, truncated, info = env.step(action.cpu().numpy().flatten())
total_reward += reward
if done or truncated:
break
print(f"Evaluation Reward: {total_reward:.2f}")Comparison with other PPO implementations:
| Implementation | Avg Reward | Training Time | Code Lines | Notes |
|---|---|---|---|---|
| This (Ours) | 2531 | 5.1h | ~500 | From scratch + height penalty |
| Stable-Baselines3 | 2450 | 6.2h | N/A | Library-based |
| CleanRL | 2380 | 5.8h | ~400 | Minimal implementation |
| SpinningUp | 2320 | 6.5h | ~600 | Educational focus |
Test conditions: NVIDIA RTX 5070 Ti, 8M timesteps, 16 parallel environments
| Coefficient | Avg Reward | Height Variance | Stability |
|---|---|---|---|
| 0.0 (Vanilla) | 2473 | 0.089 | Hopping |
| 2.0 | 2612 | 0.041 | Some hopping |
| 5.0 | 2543 | 0.023 | Mostly smooth |
| 8.0 | 2531 | 0.013 | Very smooth |
| 12.0 | 2398 | 0.008 | Too conservative |
Finding: Coefficient of 8.0 provides optimal balance between reward and stability.
| Environments | Training Time | Final Reward | Speed (steps/s) |
|---|---|---|---|
| 1 | 52.3h | 2518 | 640 |
| 4 | 14.2h | 2526 | 2,400 |
| 8 | 7.8h | 2529 | 4,600 |
| 16 | 5.1h | 2531 | 10,200 |
| 32 | 3.9h | 2527 | 11,800 |
Finding: 16 environments offer best cost-benefit. 32 envs show diminishing returns due to synchronization overhead.
-
Single Task Focus
- Trained only on Ant-v5 forward locomotion
- Not tested on other MuJoCo environments
- Lacks multi-task or transfer learning capabilities
-
Height Penalty Tuning
- Coefficient (8.0) manually tuned for Ant-v5
- May need adjustment for other quadruped robots
- Could benefit from adaptive penalty scheduling
-
Computational Requirements
- Requires 4GB+ VRAM for 16 parallel environments
- CPU-only training is 10x slower
- Rendering 2x2 demo can lag on low-end systems
-
Reproducibility Challenges
- Results vary ±50 reward across random seeds
- GPU non-determinism despite seed fixing
- TensorBoard logs consume significant disk space
-
Generalization Studies
- Test on Humanoid-v5, HalfCheetah-v5, Walker2d-v5
- Implement domain randomization for sim-to-real transfer
- Explore multi-task learning across MuJoCo suite
-
Advanced Reward Shaping
- Adaptive height penalty coefficient
- Energy efficiency bonus for joint torques
- Gait symmetry reward for natural locomotion
- Obstacle avoidance in cluttered environments
-
Algorithm Extensions
- Recurrent policies (LSTM/GRU) for partial observability
- Curiosity-driven exploration (RND, ICM)
- Hierarchical RL for complex locomotion patterns
- Model-based planning (Dreamer, MPPI)
-
Addressing Hopping Problem (Long-term)
- Automated Penalty Tuning: Use meta-learning or Bayesian optimization to find optimal height penalty coefficient without manual tuning
- Gait Library: Pre-train on diverse gait patterns (walk, trot, gallop) and fine-tune for specific tasks
- Curriculum Learning: Start with strict height penalty, gradually relax to allow natural movement
- Motion Imitation: Learn from motion capture data of real quadrupeds for biologically plausible gaits
- Residual RL: Combine classical control (PD controllers) with learned policies for stable locomotion
Contributions are welcome! Please feel free to:
- Report bugs via GitHub Issues
- Submit feature requests
- Open pull requests with improvements
- Share training results on different environments
-
Proximal Policy Optimization Algorithms
Schulman et al., 2017
arXiv:1707.06347 -
High-Dimensional Continuous Control Using Generalized Advantage Estimation
Schulman et al., 2016
arXiv:1506.02438 -
Soft Actor-Critic: Off-Policy Maximum Entropy Deep RL
Haarnoja et al., 2018
arXiv:1801.01290 -
MuJoCo: A Physics Engine for Model-Based Control
Todorov et al., 2012
IROS 2012
- OpenAI Spinning Up - RL education
- CleanRL - Single-file implementations
- Stable-Baselines3 - Production-ready algorithms
- Gymnasium - RL environment standard
This project is licensed under the MIT License - see the LICENSE file for details.
Mehmet Turan Yardımcı
- GitHub: @mturan33
- LinkedIn: Mehmet Turan Yardımcı
- Project: mujoco-ant-ppo
If you use this code in your research, please cite:
@misc{yardimci2025ppo-ant,
author = {Yardımcı, Mehmet Turan},
title = {PPO Implementation for Ant-v5 Locomotion with Height Stability},
year = {2025},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/mturan33/mujoco-ant-ppo}}
}For questions, suggestions, or collaborations:
- Open an issue: GitHub Issues
- Email: [email protected]
- LinkedIn: Connect and message me directly
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