Skip to content

Dynamic Movement Primitives Algorithms

Dynamic Movement Primitives provide a framework for learning, representing, and reproducing complex motor behaviors in robotics and control systems.

Dynamic Movement Primitives (DMPs) are a powerful framework for learning, representing, and reproducing

complex motor behaviors in robotics and control systems. DMPs provide a way to encode movements as dynamical systems that can be learned from demonstrations, adapted to new situations, and combined to create complex behaviors.

DMPs are particularly valuable in robotics because they offer a compact representation of movements that preserves the essential characteristics while allowing for generalization and adaptation. They can be used for imitation learning, skill transfer, and the generation of smooth, natural-looking movements that are robust to perturbations and can be easily modified.

Overview

Key Characteristics:

  • Dynamical System Representation

    Movements are encoded as stable dynamical systems with attractor properties

  • Learning from Demonstration

    Can learn complex movements from human demonstrations or examples

  • Generalization and Adaptation

    Learned movements can be adapted to new goals, speeds, and contexts

  • Modularity and Composition

    Simple DMPs can be combined to create complex behaviors

Common Applications:

  • manipulation

  • locomotion

  • grasping

  • assembly tasks

  • imitation learning

  • skill transfer

  • collaborative tasks

  • character animation

  • motion capture

  • procedural animation

  • prosthetics control

  • assistive devices

  • therapy robots

  • technique analysis

  • skill development

  • performance optimization

Key Concepts

  • Attractor Dynamics

    Stable dynamical systems that converge to desired states

  • Canonical System

    Time-based or state-based system that drives the movement evolution

  • Transformation System

    System that generates the actual movement trajectory

  • Forcing Function

    Nonlinear function that shapes the movement trajectory

  • Phase Variable

    Monotonic variable that tracks progress through the movement

  • Goal State

    Target state that the movement should reach

  • Start State

    Initial state from which the movement begins

  • Temporal Scaling

    Ability to speed up or slow down movements while preserving shape

Complexity Analysis

Complexity Overview

Time: O(n) to O(n²) Space: O(n) to O(n²)

Complexity depends on the number of basis functions and the dimensionality of the movement space

Discrete vs Rhythmic DMPs

Discrete DMPs:

  • For point-to-point movements
  • Converge to a goal state
  • Suitable for manipulation tasks
  • Can be temporally scaled

Rhythmic DMPs:

  • For periodic movements
  • No specific goal state
  • Suitable for locomotion and cyclic tasks
  • Maintain rhythmic patterns

DMP Learning Approaches

  1. Learning from Demonstration: Extract DMP parameters from example movements
  2. Reinforcement Learning: Optimize DMP parameters through trial and error
  3. Online Adaptation: Modify DMP parameters during execution
  4. Multi-task Learning: Learn DMPs that can handle multiple related tasks

Practical DMP Implementation

Basis Function Selection: - Gaussian basis functions are commonly used - Number of basis functions affects approximation quality - Placement and width parameters are important

Parameter Learning: - Linear regression for forcing function weights - Non-linear optimization for other parameters - Regularization to prevent overfitting

Real-time Execution: - Efficient numerical integration - Bounded computational complexity - Smooth trajectory generation

Comparison Table

Algorithm Status Time Complexity Space Complexity Difficulty Applications
DMPs with Obstacle Avoidance ❓ Unknown O(T × M) O(M) Medium Mobile Robotics, Manipulation
Spatially Coupled Bimanual DMPs ❓ Unknown O(T × K × 2) O(K × 2) Medium Assembly Tasks, Manipulation
Constrained Dynamic Movement Primitives (CDMPs) ❓ Unknown O(T × K × C) O(K + C) Medium Human-Robot Collaboration, Medical Robotics
DMPs for Human-Robot Interaction ❓ Unknown O(T × K × H) O(K × H) Medium Assistive Robotics, Collaborative Manufacturing
Multi-task DMP Learning ❓ Unknown O(T × K × N) O(K × N) Medium Household Tasks, Industrial Assembly
Geometry-aware Dynamic Movement Primitives ❓ Unknown O(T × K × n^3) O(K × n^2) Medium Impedance Control, Human-Robot Interaction
Online DMP Adaptation ❓ Unknown O(T × K × F) O(K + F) Medium Dynamic Environment Adaptation, Human-Robot Interaction
Temporal Dynamic Movement Primitives ❓ Unknown O(T × K) O(K) Medium Musical Performance, Rhythmic Locomotion
DMPs for Manipulation ❓ Unknown O(T × K × G) O(K × G) Medium Industrial Assembly, Household Tasks
Basic Dynamic Movement Primitives (DMPs) ❓ Unknown O(T × N_basis × d) O(N_basis × d) Medium Robotic Manipulation, Humanoid Robotics
Probabilistic Movement Primitives (ProMPs) ❓ Unknown O(N × T × K + K^3) O(K^2 + N × K) Medium Human-Robot Interaction, Robotic Manipulation
Hierarchical Dynamic Movement Primitives ❓ Unknown O(T × K × L) O(K × L) Medium Complex Assembly Tasks, Household Tasks
DMPs for Locomotion ❓ Unknown O(T × K × L) O(K × L) Medium Humanoid Robotics, Quadruped Robotics
Reinforcement Learning DMPs ❓ Unknown O(T × K × E) O(K + E) Medium Manipulation in Complex Environments, Navigation and Locomotion

Algorithms in This Family

  • DMPs with Obstacle Avoidance - DMPs enhanced with real-time obstacle avoidance capabilities using repulsive forces and safe navigation in cluttered environments.

  • Spatially Coupled Bimanual DMPs - DMPs for coordinated dual-arm movements with spatial coupling between arms for synchronized manipulation tasks and hand-eye coordination.

  • Constrained Dynamic Movement Primitives (CDMPs) - DMPs with safety constraints and operational requirements that ensure movements comply with safety limits and operational constraints.

  • DMPs for Human-Robot Interaction - DMPs specialized for human-robot interaction including imitation learning, collaborative tasks, and social robot behaviors.

  • Multi-task DMP Learning - DMPs that learn from multiple demonstrations across different tasks, enabling task generalization and cross-task knowledge transfer.

  • Geometry-aware Dynamic Movement Primitives - DMPs that operate with symmetric positive definite matrices to handle stiffness and damping matrices for impedance control applications.

  • Online DMP Adaptation - DMPs with real-time parameter updates, continuous learning from feedback, and adaptive behavior modification during execution.

  • Temporal Dynamic Movement Primitives - DMPs that generate time-based movements with rhythmic pattern learning, beat and tempo adaptation for temporal movement generation.

  • DMPs for Manipulation - DMPs specialized for robotic manipulation tasks including grasping movements, assembly tasks, and tool use behaviors.

  • Basic Dynamic Movement Primitives (DMPs) - Fundamental DMP framework for learning and reproducing point-to-point and rhythmic movements with temporal and spatial scaling.

  • Probabilistic Movement Primitives (ProMPs) - Probabilistic extension of DMPs that captures movement variability and generates movement distributions from multiple demonstrations.

  • Hierarchical Dynamic Movement Primitives - DMPs organized in hierarchical structures for multi-level movement decomposition, complex behavior composition, and task hierarchy learning.

  • DMPs for Locomotion - DMPs specialized for walking pattern generation, gait adaptation, and terrain-aware movement in legged robots and humanoid systems.

  • Reinforcement Learning DMPs - DMPs enhanced with reinforcement learning for parameter optimization, reward-driven learning, and policy gradient methods for movement refinement.

Implementation Status

  • Complete

    0/14 algorithms (0%)

  • Planned

    0/14 algorithms (0%)

  • Control: DMPs build upon control theory principles for stable movement generation

  • Reinforcement-Learning: RL can be used to learn and optimize DMP parameters

  • Optimization: DMP learning often involves optimization of movement parameters

  • Signal-Processing: Signal processing techniques are used for movement analysis and synthesis

References

  1. Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford (2009). Introduction to Algorithms. MIT Press

  2. Python Official Documentation. Python language reference

Tags

Dynamic Movement Primitives Algorithms for learning and reproducing movements

Control Theory Algorithms for system control and feedback

Algorithms General algorithmic concepts and implementations