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Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains
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Proposes Memory-Augmented Potential Field Theory and a Memory-Augmented MPPI controller that stores topological features of past trajectories as potential fields to escape local optima in non-convex control tasks.
Problem
Stochastic optimal controllers such as MPPI get trapped in local optima in non-convex value landscapes because they do not learn from historical trajectories.
Approach
Dynamically constructs memory-based potential fields from detected topological features (local minima, low-gradient regions, high-curvature regions) that reshape the value function via an adaptive blend with the base value, and raises the MPPI sampling temperature near remembered traps.
Key results
- MA-MPPI reaches 4978.5 on Humanoid-v4 versus 2914.2 for standard MPPI and 936.7 for SAC, as reported in the performance table.
- Local optima escape rate on Pendulum-v1 is 89.2% for MA-MPPI versus 48.3% for MPPI.
- On UAV obstacle avoidance, MA-MPPI success rate is 94.3% versus 72.8% for standard MPPI, with 12.6 ms compute time.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add memory-augmented potential fields | MPPI · Pendulum-v1 | average cumulative reward: -165.8±10.9 -> -152.4±9.7 | Helped |
| add memory-augmented potential fields | MPPI · BipedalWalker-v3 | average cumulative reward: 241.7±19.1 -> 298.4±17.2 | Helped |
| add memory-augmented potential fields | MPPI · HalfCheetah-v4 | average cumulative reward: 5027.9±148.6 -> 5893.7±156.4 | Helped |
| add memory-augmented potential fields | MPPI · Humanoid-v4 | average cumulative reward: 2914.2±318.7 -> 4978.5±283.1 | Helped |
| add memory-augmented potential fields | MPPI · Pendulum-v1 | local optima escape rate: 48.3±5.7 -> 89.2±4.1 | Helped |
| add memory-augmented potential fields | MPPI · BipedalWalker-v3 | local optima escape rate: 41.6±6.4 -> 83.5±5.2 | Helped |
| add memory-augmented potential fields | MPPI · HalfCheetah-v4 | local optima escape rate: 36.2±7.2 -> 76.8±6.4 | Helped |
| add memory-augmented potential fields | MPPI · Humanoid-v4 | local optima escape rate: 29.4±8.6 -> 72.3±7.8 | Helped |
| add memory augmentation | Standard MPPI · IEEE 39-bus New England test system | disturbance recovery time: 8.7 -> 4.2 | Helped |
| add memory augmentation | Standard MPPI · UAV obstacle avoidance | success rate: 72.8 -> 94.3 | Helped |
| add memory augmentation | Standard MPPI · UAV obstacle avoidance | local minima escapes: 34.2 -> 87.5 | Helped |
| remove memory (ablation) | MA-MPPI · robotic control environments | performance: 42-58% performance decrease | Hurt |
Surprising findings
- Standard MPPI in the UAV experiment is faster (10.2 ms) than MA-MPPI, which is the only compute metric where MA-MPPI is not best in the power system and UAV tables.
Limitations
- Assumes full-state feedback; state-estimation uncertainty not addressed.
- Restricted generalization between similar features and lacks sophisticated memory management for long operation.
- Theoretical proofs rely on loose assumptions (e.g., biased random walk approximation, independence) and the escape/convergence claims are not rigorously established.
Experimental setup
Datasets: Pendulum-v1 BipedalWalker-v3 HalfCheetah-v4 Humanoid-v4 IEEE 39-bus New England test system
Benchmarks: Pendulum-v1 BipedalWalker-v3 HalfCheetah-v4 Humanoid-v4 IEEE 39-bus New England power system UAV obstacle avoidance
Metrics: average cumulative reward local optima escape rate constraint violation rate disturbance recovery time success rate compute time
Baselines: MPPI SAC PPO DDPG iLQR MPC Diffusion Policy Motion Transformer MLP-based MPC DKO-based MPC
Builds on: Model Predictive Path Integral control navigation functions Neural Episodic Control
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