Online DMP Adaptation
Online DMP Adaptation
DMPs with real-time parameter updates, continuous learning from feedback, and adaptive behavior modification during execution.
Family: Dynamic Movement Primitives Status: 📋 Planned
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Overview
Online DMP Adaptation extends the basic DMP framework to enable real-time parameter updates and continuous learning from feedback during movement execution. This approach allows robots to adapt their movements based on environmental changes, task requirements, and performance feedback without requiring complete re-learning.
The key innovation of online DMP adaptation is the integration of: - Real-time parameter updates during movement execution - Continuous learning from sensory feedback and performance metrics - Adaptive behavior modification based on changing conditions - Incremental learning that preserves previously learned behaviors - Robust adaptation mechanisms that handle noisy feedback
These DMPs are particularly valuable in applications requiring adaptation to changing environments, such as manipulation in dynamic environments, human-robot interaction, and any task where the robot must continuously improve its performance.
Mathematical Formulation¶
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Problem Definition
Given:
- Basic DMP: τẏ = α_y(β_y(g - y) - ẏ) + f(x)
- Feedback signal: F(t) = {f_sensor(t), f_performance(t), f_environment(t)}
- Adaptation rate: η > 0
- Learning rate: α_learn > 0
- Forgetting factor: λ ∈ [0,1]
The online adaptation becomes: τẏ = α_y(β_y(g - y) - ẏ) + f(x, w(t))
Where the weights are updated online: w(t+1) = w(t) + η * ∇_w J(w(t), F(t))
And the objective function is: J(w, F) = α_learn * L_performance(w, F) + λ * L_consistency(w, w_old)
Where: - L_performance is the performance loss - L_consistency is the consistency loss with previous weights
Key Properties
Online Weight Update
w(t+1) = w(t) + η * ∇_w J(w(t), F(t))
Weights are updated in real-time based on feedback
Performance Learning
L_performance(w, F) = ||y_desired - y_actual||²
Learning is driven by performance feedback
Consistency Preservation
L_consistency(w, w_old) = ||w - w_old||²
Previous knowledge is preserved through consistency
Key Properties¶
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Real-time Adaptation
Adapts parameters in real-time during execution
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Continuous Learning
Continuously learns from feedback and experience
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Incremental Updates
Updates parameters incrementally without complete re-learning
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Feedback Integration
Integrates multiple types of feedback for adaptation
Implementation Approaches¶
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Online DMP adaptation using gradient-based parameter updates
Complexity:
- Time: O(T × K × F)
- Space: O(K + F)
Advantages
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Real-time parameter updates
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Continuous learning from feedback
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Incremental adaptation
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Multiple feedback integration
Disadvantages
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Requires feedback functions
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May be sensitive to noisy feedback
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Computational overhead
Online DMP adaptation using reinforcement learning
Complexity:
- Time: O(T × K × A)
- Space: O(K + A)
Advantages
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Reinforcement learning integration
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Reward-based adaptation
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Experience-based learning
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Policy gradient methods
Disadvantages
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Requires reward function design
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May be slow to converge
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Sensitive to reward shaping
Complete Implementation
The full implementation with error handling, comprehensive testing, and additional variants is available in the source code:
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Main implementation with gradient-based and RL adaptation:
src/algokit/dynamic_movement_primitives/online_adaptation_dmps.py -
Comprehensive test suite including adaptation tests:
tests/unit/dynamic_movement_primitives/test_online_adaptation_dmps.py
Complexity Analysis¶
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Time & Space Complexity Comparison
| Approach | Time Complexity | Space Complexity | Notes |
|---|---|---|---|
| Gradient-based Adaptation | O(T × K × F) | O(K + F) | Time complexity scales with trajectory length, basis functions, and feedback functions |
Use Cases & Applications¶
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Application Categories
Dynamic Environment Adaptation
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Changing Obstacles: Adapting to moving or changing obstacles
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Variable Surfaces: Adapting to different surface properties
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Weather Conditions: Adapting to changing weather conditions
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Lighting Changes: Adapting to changing lighting conditions
Human-Robot Interaction
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Adaptive Assistance: Adapting assistance based on user needs
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Collaborative Tasks: Adapting to human partner behavior
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Learning from Humans: Learning from human demonstrations and feedback
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Personalized Interaction: Personalizing interaction based on user preferences
Manufacturing and Assembly
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Quality Control: Adapting to quality requirements
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Product Variations: Adapting to different product specifications
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Tool Wear: Adapting to tool wear and degradation
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Process Optimization: Optimizing processes based on performance
Service Robotics
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Household Tasks: Adapting to different household environments
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Cleaning: Adapting cleaning strategies based on results
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Cooking: Adapting cooking techniques based on taste feedback
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Maintenance: Adapting maintenance procedures based on equipment condition
Medical and Rehabilitation
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Patient Adaptation: Adapting to individual patient needs
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Recovery Progress: Adapting to patient recovery progress
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Therapy Optimization: Optimizing therapy based on patient response
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Surgical Adaptation: Adapting surgical procedures based on patient anatomy
Educational Value
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Online Learning: Understanding online learning and adaptation
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Feedback Integration: Understanding how to integrate multiple feedback sources
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Reinforcement Learning: Understanding RL-based adaptation
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Continuous Improvement: Understanding continuous improvement mechanisms
References & Further Reading¶
:material-library: Core Papers
:material-web: Online Learning
:material-web: Online Resources
:material-code-tags: Implementation & Practice
Interactive Learning
Try implementing the different approaches yourself! This progression will give you deep insight into the algorithm's principles and applications.
Pro Tip: Start with the simplest implementation and gradually work your way up to more complex variants.
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Navigation¶
Related Algorithms in Dynamic Movement Primitives:
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DMPs with Obstacle Avoidance - DMPs enhanced with real-time obstacle avoidance capabilities using repulsive forces and safe navigation in cluttered environments.
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Spatially Coupled Bimanual DMPs - DMPs for coordinated dual-arm movements with spatial coupling between arms for synchronized manipulation tasks and hand-eye coordination.
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Constrained Dynamic Movement Primitives (CDMPs) - DMPs with safety constraints and operational requirements that ensure movements comply with safety limits and operational constraints.
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DMPs for Human-Robot Interaction - DMPs specialized for human-robot interaction including imitation learning, collaborative tasks, and social robot behaviors.
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Multi-task DMP Learning - DMPs that learn from multiple demonstrations across different tasks, enabling task generalization and cross-task knowledge transfer.
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Geometry-aware Dynamic Movement Primitives - DMPs that operate with symmetric positive definite matrices to handle stiffness and damping matrices for impedance control applications.
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Temporal Dynamic Movement Primitives - DMPs that generate time-based movements with rhythmic pattern learning, beat and tempo adaptation for temporal movement generation.
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DMPs for Manipulation - DMPs specialized for robotic manipulation tasks including grasping movements, assembly tasks, and tool use behaviors.
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Basic Dynamic Movement Primitives (DMPs) - Fundamental DMP framework for learning and reproducing point-to-point and rhythmic movements with temporal and spatial scaling.
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Probabilistic Movement Primitives (ProMPs) - Probabilistic extension of DMPs that captures movement variability and generates movement distributions from multiple demonstrations.
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Hierarchical Dynamic Movement Primitives - DMPs organized in hierarchical structures for multi-level movement decomposition, complex behavior composition, and task hierarchy learning.
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DMPs for Locomotion - DMPs specialized for walking pattern generation, gait adaptation, and terrain-aware movement in legged robots and humanoid systems.
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Reinforcement Learning DMPs - DMPs enhanced with reinforcement learning for parameter optimization, reward-driven learning, and policy gradient methods for movement refinement.