Multi-Task DMP Learning
Multi-task DMP Learning
DMPs that learn from multiple demonstrations across different tasks, enabling task generalization and cross-task knowledge transfer.
Family: Dynamic Movement Primitives Status: 📋 Planned
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Overview
Multi-task DMP Learning extends the basic DMP framework to handle learning from multiple demonstrations across different tasks, enabling task generalization and cross-task knowledge transfer. This approach allows robots to learn common movement patterns across tasks and transfer knowledge between related tasks.
The key innovation of multi-task DMP learning is the integration of: - Learning from multiple demonstrations across different tasks - Task generalization through shared representation learning - Cross-task knowledge transfer mechanisms - Task-specific and shared parameter learning - Robust performance across diverse task domains
These DMPs are particularly valuable in applications requiring robots to perform multiple related tasks, such as household chores, industrial assembly, and any scenario where tasks share common movement patterns.
Mathematical Formulation¶
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Problem Definition
Given:
- Multiple tasks: T = {T_1, T_2, ..., T_N}
- Demonstrations for each task: D_i = {d_i^1, d_i^2, ..., d_i^M_i} for task T_i
- Shared DMP parameters: θ_shared
- Task-specific parameters: θ_i for task T_i
- Task similarity matrix: S = {s_ij} where s_ij is similarity between tasks T_i and T_j
The multi-task learning objective is: min_{θ_shared, θ_1, ..., θ_N} Σ_{i=1}^N L_i(θ_shared, θ_i) + λ_shared * R_shared(θ_shared) + λ_task * Σ_{i=1}^N R_task(θ_i)
Where: - L_i is the loss for task T_i - R_shared is the regularization for shared parameters - R_task is the regularization for task-specific parameters - λ_shared and λ_task are regularization weights
Key Properties
Shared Representation
θ_shared = argmin Σ_{i=1}^N L_i(θ_shared, θ_i)
Shared parameters capture common patterns across tasks
Task-specific Adaptation
θ_i = argmin L_i(θ_shared, θ_i) + λ_task * R_task(θ_i)
Task-specific parameters adapt to individual task requirements
Knowledge Transfer
θ_i = θ_shared + Δθ_i where Δθ_i is task-specific adaptation
Knowledge is transferred through shared parameters
Key Properties¶
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Multi-task Learning
Learns from multiple tasks simultaneously
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Task Generalization
Generalizes learned patterns across tasks
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Knowledge Transfer
Transfers knowledge between related tasks
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Shared Representation
Learns shared representations across tasks
Implementation Approaches¶
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Multi-task DMPs with shared representation learning
Complexity:
- Time: O(T × K × N)
- Space: O(K × N)
Advantages
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Multi-task learning capability
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Shared representation learning
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Task generalization
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Knowledge transfer between tasks
Disadvantages
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Higher computational cost
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Requires multiple task demonstrations
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Complex parameter tuning
Multi-task DMPs with explicit transfer learning mechanisms
Complexity:
- Time: O(T × K × N + N²)
- Space: O(K × N + N²)
Advantages
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Explicit transfer learning mechanisms
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Task similarity-based transfer
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Transfer matrix learning
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Improved knowledge transfer
Disadvantages
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Higher computational cost
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Requires task similarity estimation
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Complex transfer mechanisms
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 shared representation and transfer learning:
src/algokit/dynamic_movement_primitives/multi_task_dmp_learning.py -
Comprehensive test suite including multi-task learning tests:
tests/unit/dynamic_movement_primitives/test_multi_task_dmp_learning.py
Complexity Analysis¶
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Time & Space Complexity Comparison
| Approach | Time Complexity | Space Complexity | Notes |
|---|---|---|---|
| Shared Representation Learning | O(T × K × N) | O(K × N) | Time complexity scales with trajectory length, basis functions, and number of tasks |
Use Cases & Applications¶
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Application Categories
Household Tasks
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Cooking: Learning cooking skills across different recipes
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Cleaning: Learning cleaning techniques for different surfaces
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Laundry: Learning laundry tasks for different fabric types
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Gardening: Learning gardening techniques for different plants
Industrial Assembly
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Product Assembly: Learning assembly techniques for different products
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Quality Control: Learning quality control procedures for different components
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Packaging: Learning packaging techniques for different products
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Maintenance: Learning maintenance procedures for different equipment
Service Robotics
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Healthcare: Learning healthcare procedures for different patients
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Education: Learning educational techniques for different subjects
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Entertainment: Learning entertainment skills for different audiences
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Security: Learning security procedures for different environments
Human-Robot Interaction
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Collaborative Tasks: Learning collaborative techniques with different partners
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Assistive Tasks: Learning assistive techniques for different users
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Social Interaction: Learning social interaction skills for different contexts
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Learning Tasks: Learning teaching techniques for different learners
Manufacturing
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Production: Learning production techniques for different products
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Quality Control: Learning quality control procedures for different standards
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Logistics: Learning logistics procedures for different supply chains
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Safety: Learning safety procedures for different work environments
Educational Value
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Multi-task Learning: Understanding multi-task learning principles
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Transfer Learning: Understanding transfer learning mechanisms
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Shared Representation: Understanding shared representation learning
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Task Generalization: Understanding task generalization techniques
References & Further Reading¶
:material-library: Core Papers
:material-library: Multi-task 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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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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Online DMP Adaptation - DMPs with real-time parameter updates, continuous learning from feedback, and adaptive behavior modification during execution.
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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.