Spatially-Coupled Bimanual DMPs
Spatially Coupled Bimanual DMPs
DMPs for coordinated dual-arm movements with spatial coupling between arms for synchronized manipulation tasks and hand-eye coordination.
Family: Dynamic Movement Primitives Status: 📋 Planned
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Overview
Spatially Coupled Bimanual DMPs extend the basic DMP framework to handle coordinated dual-arm movements where the two arms must work together in a synchronized manner. This approach enables complex manipulation tasks that require both arms to coordinate their movements spatially and temporally.
The key innovation of spatially coupled bimanual DMPs is the integration of: - Spatial coupling between the two arms through coupling terms - Synchronized movement execution with temporal coordination - Hand-eye coordination for precise manipulation tasks - Adaptive coupling strength based on task requirements - Robust coordination even in the presence of disturbances
These DMPs are particularly valuable in applications requiring coordinated manipulation, such as assembly tasks, object manipulation, tool use, and complex manipulation behaviors that cannot be performed with a single arm.
Mathematical Formulation¶
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Problem Definition
Given:
- Left arm DMP: τẏ_L = α_y(β_y(g_L - y_L) - ẏ_L) + f_L(x_L) + C_L(y_R, ẏ_R)
- Right arm DMP: τẏ_R = α_y(β_y(g_R - y_R) - ẏ_R) + f_R(x_R) + C_R(y_L, ẏ_L)
- Coupling functions: C_L(y_R, ẏ_R) and C_R(y_L, ẏ_L)
- Coupling strength: k_couple
- Synchronization parameter: τ_sync
The spatially coupled bimanual DMPs are: τẏ_L = α_y(β_y(g_L - y_L) - ẏ_L) + f_L(x_L) + k_couple * C_L(y_R, ẏ_R) τẏ_R = α_y(β_y(g_R - y_R) - ẏ_R) + f_R(x_R) + k_couple * C_R(y_L, ẏ_L)
Where the coupling functions ensure spatial coordination: C_L(y_R, ẏ_R) = k_spatial * (y_R - y_L) + k_velocity * (ẏ_R - ẏ_L) C_R(y_L, ẏ_L) = k_spatial * (y_L - y_R) + k_velocity * (ẏ_L - ẏ_R)
Key Properties
Spatial Coupling
C_L(y_R, ẏ_R) = k_spatial * (y_R - y_L) + k_velocity * (ẏ_R - ẏ_L)
Coupling function that maintains spatial relationships between arms
Synchronization
τ_sync = τ_L = τ_R
Temporal synchronization parameter ensures both arms move in sync
Adaptive Coupling
k_couple = k_couple(t) based on task requirements
Coupling strength can be adapted based on task phase
Key Properties¶
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Dual-Arm Coordination
Coordinates movements of both arms simultaneously
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Spatial Coupling
Maintains spatial relationships between arms
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Temporal Synchronization
Synchronizes movement timing between arms
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Hand-Eye Coordination
Coordinates arm movements with visual feedback
Implementation Approaches¶
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Basic spatially coupled bimanual DMPs with position and velocity coupling
Complexity:
- Time: O(T × K × 2)
- Space: O(K × 2)
Advantages
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Natural bimanual coordination
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Spatial and temporal coupling
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Adaptive coupling strength
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Smooth trajectory generation
Disadvantages
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Higher computational cost
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Requires careful parameter tuning
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May not handle all coordination patterns
Bimanual DMPs with hand-eye coordination for precise manipulation
Complexity:
- Time: O(T × K × 2 + T × V)
- Space: O(K × 2 + V)
Advantages
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Hand-eye coordination
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Visual feedback integration
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Precise manipulation capabilities
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Adaptive to visual targets
Disadvantages
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Requires visual feedback system
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Higher computational cost
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Sensitive to visual noise
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 spatially coupled and hand-eye coordination DMPs:
src/algokit/dynamic_movement_primitives/bimanual_dmps.py -
Comprehensive test suite including coordination tests:
tests/unit/dynamic_movement_primitives/test_bimanual_dmps.py
Complexity Analysis¶
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Time & Space Complexity Comparison
| Approach | Time Complexity | Space Complexity | Notes |
|---|---|---|---|
| Basic Bimanual DMP | O(T × K × 2) | O(K × 2) | Time complexity scales with trajectory length, basis functions, and two arms |
Use Cases & Applications¶
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Application Categories
Assembly Tasks
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Bimanual Assembly: Assembling parts that require both hands
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Precision Assembly: Precise assembly tasks with hand-eye coordination
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Complex Assembly: Complex assembly tasks with multiple components
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Quality Control: Quality control tasks requiring both hands
Manipulation
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Object Manipulation: Manipulating large or complex objects
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Tool Use: Using tools that require both hands
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Packaging: Packaging tasks requiring coordinated movements
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Sorting: Sorting tasks with coordinated hand movements
Human-Robot Interaction
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Collaborative Tasks: Working with humans on collaborative tasks
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Handover: Handing over objects between human and robot
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Assistive Tasks: Assisting humans with tasks requiring both hands
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Social Interaction: Social interaction tasks with coordinated movements
Service Robotics
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Household Tasks: Household tasks requiring both hands
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Cooking: Cooking tasks with coordinated hand movements
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Cleaning: Cleaning tasks requiring both hands
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Maintenance: Maintenance tasks with coordinated movements
Industrial Automation
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Manufacturing: Manufacturing tasks requiring both hands
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Quality Control: Quality control tasks with coordinated movements
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Packaging: Packaging tasks requiring both hands
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Inspection: Inspection tasks with coordinated movements
Educational Value
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Bimanual Coordination: Understanding how to coordinate dual-arm movements
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Spatial Coupling: Understanding spatial coupling between robotic systems
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Hand-Eye Coordination: Understanding hand-eye coordination in robotics
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Multi-Agent Systems: Understanding coordination in multi-agent systems
References & Further Reading¶
:material-library: Core Papers
:material-library: Bimanual Coordination
: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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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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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.