Dynamic Neural Potential Field: Online Trajectory Optimization in the Presence of Moving Obstacles

1. Problem Statement

Autonomous mobile robots operating in human-centric environments (homes, offices, warehouses) face significant challenges in local trajectory planning when dynamic obstacles (e.g., walking humans) are present.

• The Challenge: Traditional Model Predictive Control (MPC) requires an analytical representation of collision risks (repulsive potentials) to optimize trajectories. However, in dynamic scenes, the obstacle map changes over time.
• Limitations of Existing Methods:
  • Geometric MPC: Approximating obstacles with simple shapes (circles, rectangles) loses fidelity and struggles with complex, high-resolution occupancy grids.
  • Sampling-based (MPPI): Can handle arbitrary maps but often produces chattering solutions and is computationally expensive.
  • Neural Approaches: Previous neural collision models often focus on static scenes or require non-real-time training/inference, failing to provide differentiable, real-time potentials for dynamic obstacles within an MPC loop.
• Goal: Develop a framework that learns spatiotemporal collision risks from raw occupancy grids and dynamic obstacle states, producing differentiable repulsive potentials that can be injected directly into a real-time MPC solver.

2. Methodology: NPField-GPT Framework

The authors propose NPField-GPT (Dynamic Neural Potential Field), a hybrid framework that couples classical MPC with a Transformer-based predictor. The core philosophy is to learn only the collision risk while keeping the optimization model-based.

A. System Architecture

The framework integrates three neural variants to balance accuracy and latency:

1. NPField-StaticMLP: Treats dynamic scenes as a sequence of static maps. It processes one time step at a time.
2. NPField-DynamicMLP: Uses parallel Multi-Layer Perceptron (MLP) heads to predict future potentials concurrently, conditioned on dynamic obstacle states.
3. NPField-GPT (The Primary Contribution):
   • Backbone: Uses a non-autoregressive Transformer.
   • Input Tokens: The model constructs a token sequence including:
     • Map embedding (CNN + spatial self-attention on occupancy grid).
     • Robot footprint embedding.
     • Dynamic obstacle state ($x, y, \theta$).
     • Query robot state ($x, y, \theta$).
     • Learnable Query Tokens: 10 learnable vectors representing the prediction horizon.
   • Mechanism: Instead of autoregressively predicting step $t+1$ from $t$, the Transformer predicts the entire potential horizon in a single forward pass. The query tokens attend to the context (map, robot, and obstacle states), allowing the model to capture complex spatiotemporal dependencies holistically.
   • Output: A sequence of differentiable repulsive potentials for the MPC horizon.

B. Integration with MPC

• Differentiability: The neural model is wrapped using L4CasADi, providing an exact symbolic description of the neural network. This allows the predicted potentials to be used as a cost term in a Sequential Quadratic Programming (SQP) solver (Acados).
• Optimization: The MPC minimizes a cost function comprising:
  1. Path following error.
  2. Control effort minimization.
  3. Neural Repulsive Potential: The learned cost term that penalizes proximity to obstacles based on the robot's footprint.
• Training: The model is trained to minimize a weighted Mean Squared Error (MSE) between predicted and reference potentials (derived from Signed Distance Functions). A distance-dependent weighting scheme emphasizes errors near obstacles. An auxiliary occupancy reconstruction loss is used during training to stabilize spatial embeddings but is removed at inference.

C. Multi-Obstacle Handling

The framework naturally extends to multiple dynamic obstacles via additive superposition. The model predicts potentials for each obstacle independently, and the results are summed ($J_{multi} = \sum J_j$) without requiring architectural changes or retraining.

3. Key Contributions

1. Real-Time Dynamic Neural Potential Framework: A novel MPC-compatible system with three variants (StaticMLP, DynamicMLP, GPT) addressing the accuracy-latency trade-off.
2. NPField-GPT Architecture: A Transformer-based approach that predicts the full potential horizon in parallel using learnable query tokens, significantly improving the representation of spatiotemporal obstacle dynamics compared to sequential methods.
3. Differentiable Integration: Successful integration of neural costs into an Acados MPC solver via L4CasADi, enabling gradient-based optimization with learned collision risks.
4. Comprehensive Evaluation: Extensive benchmarking against state-of-the-art methods (CIAO*, MPPI) in simulation (BenchMR) and on a real Husky UGV in office corridors.

4. Experimental Results

The authors evaluated the methods on 100 dynamic scenarios and real-world robot tests.

• Performance Metrics:
  • Safety: NPField-GPT achieved the highest safety distance (0.115m) and lowest path length (2.06m), indicating smoother and safer navigation.
  • Efficiency: NPField-GPT had the lowest "Angle-Over-Length" (AOL) metric (0.015), signifying the smoothest trajectory.
  • Latency:
    • StaticMLP was the fastest (366 ms) but less safe.
    • NPField-GPT had higher latency (663 ms) due to the Transformer backbone but offered superior trajectory quality.
    • MPPI was fast but produced inferior trajectories (higher path length, lower safety).
    • CIAO* (State-of-the-art baseline) performed well but was slower than StaticMLP and less safe than NPField-GPT.
• Qualitative Analysis:
  • StaticMLP tended to merge dynamic obstacles with walls, losing boundary definition.
  • DynamicMLP produced diffuse boundaries.
  • NPField-GPT maintained sharp, accurate boundaries for both static walls and moving obstacles throughout the prediction horizon.
• Real-World Deployment: Successfully deployed on a Husky UGV in office corridors, demonstrating real-time replanning and collision avoidance with moving obstacles.

5. Significance and Conclusion

• Paradigm Shift: The work demonstrates that learning-based components can be effectively integrated into classical optimization loops (MPC) to handle complex dynamic environments without sacrificing stability or transparency.
• Practical Impact: It solves the "fidelity vs. speed" dilemma in dynamic obstacle avoidance. While geometric approximations are fast but inaccurate, and sampling methods are flexible but unstable, NPField-GPT offers a middle ground: high-fidelity, differentiable risk modeling that is fast enough for indoor mobile robots (replanning at ~1.5 Hz).
• Future Work: The authors note that while the method is robust, it lacks theoretical safety guarantees (being learning-based). Future directions include integrating uncertainty-aware models and advanced motion predictors to further enhance safety and interaction modeling.

Availability: The code and trained models are open-source at the provided GitHub repository.