Meta QLearning experiments to optimize robot walking patterns.

Implemented Meta-Q-Learning for optimizing humanoid walking patterns. The project also demonstrate its effectiveness in improving stability, efficiency, and adaptability. Additionally, this work also explores the transferability of Meta-Q-Learning to new tasks with minimal tuning.

Conducted experiments: Test how adaptable the humanoid is by performing:

  1. Side stepping
  2. Ascending and Descending

Theoretical Framework

Meta-Learning in Reinforcement Learning

Meta-learning, or “learning to learn,” is particularly powerful in reinforcement learning scenarios where we want an agent to quickly adapt to new tasks. In the context of humanoid robotics, this means learning a policy that can rapidly adapt to different walking patterns, terrains, and disturbances.

The Meta Q-Learning approach we implemented combines several key concepts:

  1. Task Distribution:
    • We define a distribution of tasks (different walking patterns, terrains, and disturbances)
    • Each task represents a different MDP (Markov Decision Process) with shared structure
    • The agent learns to quickly adapt to new tasks from this distribution
  2. Meta-Policy Architecture:
    • The meta-policy consists of two components:
      • A task-agnostic base policy that captures common walking patterns
      • A task-specific adaptation mechanism that modifies the base policy for new tasks
    • This architecture enables rapid adaptation to new scenarios

  3. Optimization Objective: The meta-learning objective can be expressed as:

    $\min_{\theta} \mathbb{E}_{T \sim p(T)}[L_T(\theta)]$

    where:

    • $\theta$ represents the meta-parameters
    • $p(T)$ is the task distribution
    • $L_T$ is the loss function for task T

Implementation Details

  1. State Space:
    • Joint angles and velocities
    • Center of mass position and velocity
    • Contact forces
    • Task-specific features (terrain height, disturbance magnitude)
  2. Action Space:
    • Joint torques
    • Desired joint positions
    • Balance control parameters

  3. Reward Function: The reward function combines multiple objectives:

    $R = w_1R_{\text{stability}} + w_2R_{\text{energy}} + w_3R_{\text{task}}$

    where:

    • $R_{\text{stability}}$: Penalizes deviations from stable walking
    • $R_{\text{energy}}$: Encourages energy-efficient movements
    • $R_{\text{task}}$: Rewards task-specific objectives
  4. Meta-Learning Algorithm: We use a variant of Model-Agnostic Meta-Learning (MAML) adapted for Q-learning:
    • Inner loop: Task-specific adaptation using Q-learning
    • Outer loop: Meta-parameter updates using gradient descent
    • The adaptation process can be expressed as:

    $\theta’ = \theta - \alpha\nabla_{\theta}L_T(\theta)$

    where $\alpha$ is the adaptation rate

Transfer Learning Mechanism

The key to successful transfer learning in our implementation is the hierarchical structure of the policy:

  1. Base Policy Layer:
    • Learns fundamental walking patterns
    • Captures common dynamics across tasks
    • Provides a stable starting point for adaptation
  2. Adaptation Layer:
    • Modifies the base policy for specific tasks
    • Uses task-specific features to guide adaptation
    • Enables rapid learning of new behaviors

This hierarchical structure allows the agent to:

  • Maintain stable walking patterns while adapting to new tasks
  • Transfer knowledge between similar tasks
  • Learn new tasks with minimal data

Inference

This work was done as a fun project to learn RL and its applications, so I have not drawn a lot of theoretical inferences. That being said, here are some quantitative inferences from the work: out out

Code repository: Feel free to browse and access the software stack: https://github.com/gokulp01/meta-qlearning-humanoid