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Lesson 12.1: Humanoid Robot Locomotion

Learning Objectives​

After completing this lesson, you will be able to:

  • Understand the fundamental principles of legged locomotion in humanoid robots
  • Analyze different walking gaits and their characteristics
  • Design footstep planning algorithms for stable locomotion
  • Evaluate dynamic stability during locomotion
  • Compare various approaches to humanoid walking control

Introduction​

Humanoid robot locomotion is one of the most challenging aspects of humanoid robotics, requiring the robot to move efficiently and stably on two legs. Unlike wheeled or tracked robots, humanoid robots must dynamically balance their center of mass while transferring weight from one foot to another. This lesson explores the principles of legged locomotion, walking gaits, footstep planning, and dynamic stability considerations that enable humanoid robots to move through their environment.

Fundamentals of Legged Locomotion​

Basic Concepts​

Locomotion vs. Mobility

  • Locomotion: The act of moving from one place to another
  • Mobility: The ability to move freely and easily
  • For humanoid robots, locomotion specifically refers to walking, running, or other leg-based movement patterns

Support Phases

  • Single Support: One foot is in contact with the ground
  • Double Support: Both feet are in contact with the ground
  • Flight Phase: Neither foot is in contact (in running)

Gait Cycle

  • The complete sequence of movements that constitutes one step
  • Includes both stance and swing phases
  • Characterized by duty factor (percentage of cycle in contact)

Key Parameters in Locomotion​

Step Parameters

  • Step Length: Distance between consecutive foot placements
  • Step Width: Lateral distance between feet
  • Step Time: Duration of one complete step cycle
  • Stride Length: Distance between two consecutive placements of the same foot

Dynamic Parameters

  • Walking Speed: Forward velocity of the robot
  • Cadence: Steps per unit time
  • Duty Factor: Fraction of gait cycle in contact with ground

Walking Gaits in Humanoid Robots​

Static vs. Dynamic Walking​

Static Walking

  • Maintains static stability throughout the gait cycle
  • Center of mass (CoM) remains within the support polygon at all times
  • Conservative approach with slower speeds
  • Suitable for initial development and safety-critical applications

Dynamic Walking

  • Allows temporary instability during gait cycle
  • More human-like and energy efficient
  • Requires sophisticated balance control
  • Enables faster walking speeds

Common Walking Patterns​

Periodic Gaits

  • Repetitive patterns that cycle continuously
  • Symmetric: Both legs follow identical patterns
  • Asymmetric: Different patterns for each leg

Gait Classification by Stability

  • Stable Gaits: Always maintain balance during motion
  • Limit Cycles: Repeat the same pattern after perturbations
  • Chaotic Gaits: Highly dynamic but controlled motion

Walking Gait Generation Methods​

Predefined Trajectory Methods

  • Use precomputed joint angle trajectories
  • Simple to implement and execute
  • Limited adaptability to disturbances
  • Good for consistent terrain conditions

Model-Based Gait Generation

  • Uses dynamic models (LIPM, inverted pendulum)
  • Generates gaits based on physical constraints
  • Better stability properties
  • More adaptable to different conditions

**Learning-Based Approits

  • Trained on human walking data or through reinforcement learning
  • Can achieve more natural movement patterns
  • Requires extensive training data
  • May be difficult to interpret and tune

Footstep Planning​

Planning Framework​

Footstep planning determines where and when to place the feet during locomotion. This is crucial for:

  • Maintaining balance during walking
  • Navigating through cluttered environments
  • Adapting to terrain variations
  • Achieving desired walking speeds

Grid-Based Planning​

Discretized Grid Approach

  • Divide the environment into a grid of possible foot positions
  • Use pathfinding algorithms (A*, Dijkstra) to find optimal footstep sequence
  • Simple to implement and visualize
  • May miss optimal continuous solutions

Advantages and Disadvantages

  • Advantages: Computationally efficient, easy to incorporate obstacles
  • Disadvantages: Discretization errors, limited precision

Sampling-Based Planning​

RRT (Rapidly-exploring Random Tree)

  • Builds a tree of possible footstep sequences
  • Explores the configuration space randomly
  • Good for complex environments with many obstacles
  • Probabilistically complete

PRM (Probabilistic Roadmap)

  • Precomputes a roadmap of possible foot positions
  • Queries the roadmap during execution
  • Good for repeated planning in similar environments

Optimization-Based Planning​

Trajectory Optimization

  • Formulates footstep planning as an optimization problem
  • Minimizes cost function (energy, time, stability)
  • Incorporates constraints (balance, kinematic limits)
  • Computationally intensive but very flexible

Dynamic Stability in Locomotion​

Stability Metrics​

Zero Moment Point (ZMP)

  • Critical metric for dynamic stability
  • Must remain within support polygon for stability
  • Used in most humanoid walking controllers

Capture Point

  • Location where robot can come to rest given current state
  • Useful for gait planning and disturbance recovery
  • Provides intuitive understanding of stability margins

Foot Rotation Indicator (FRI)

  • Measures the point of force application on the foot
  • Indicates stability during single support phase
  • Useful for real-time balance assessment

Stability Control During Locomotion​

Predictive Control

  • Uses future trajectory information to improve stability
  • Anticipates balance requirements
  • Reduces tracking errors

Feedback Control

  • Corrects for deviations from planned trajectory
  • Maintains stability in presence of disturbances
  • Provides robustness to model uncertainties

Hybrid Control Approaches

  • Combines predictive and feedback elements
  • Optimizes for both stability and performance
  • Adapts to changing conditions

Walking Control Strategies​

Cartesian Space Control​

End-Effector Based Control

  • Controls foot positions and orientations directly
  • Ensures precise foot placement
  • Requires inverse kinematics solutions

Center of Mass Control

  • Directly controls CoM trajectory
  • Ensures balance throughout gait
  • Often combined with ZMP control

Joint Space Control​

Inverse Dynamics Control

  • Computes required joint torques for desired motion
  • Accounts for robot dynamics
  • Provides precise motion control

Impedance Control

  • Modifies apparent stiffness and damping of joints
  • Enables compliant interaction with environment
  • Improves stability during contact transitions

Terrain Adaptation​

Flat Ground Walking​

  • Simplest locomotion scenario
  • Precomputed gaits can be highly effective
  • Focus on stability and efficiency

Uneven Terrain​

Terrain Mapping

  • Uses sensors to identify terrain characteristics
  • Plans foot placement to avoid obstacles
  • Adjusts gait parameters for stability

Adaptive Control

  • Modifies gait based on terrain feedback
  • Adjusts step height for obstacles
  • Changes walking speed for stability

Stair Climbing and Descending​

Specialized Gait Patterns

  • Different gaits for ascending and descending
  • Requires precise foot placement control
  • Enhanced stability control for vertical transitions

Challenges in Humanoid Locomotion​

Physical Constraints​

Actuator Limitations

  • Torque and speed constraints limit gait options
  • Energy consumption affects walking duration
  • Heat dissipation affects performance

Structural Limitations

  • Joint range of motion constrains gait patterns
  • Weight distribution affects stability
  • Structural compliance affects control

Environmental Challenges​

Surface Variations

  • Different friction coefficients affect gait
  • Soft surfaces require different control strategies
  • Slippery surfaces increase fall risk

Obstacle Navigation

  • Requires real-time planning capabilities
  • Integration with perception systems
  • Dynamic replanning when needed

Control Complexity​

High-Dimensional Systems

  • 30+ degrees of freedom in typical humanoid
  • Coordination of multiple limbs required
  • Real-time computation constraints

Uncertainty Handling

  • Model inaccuracies affect control
  • Sensor noise impacts feedback
  • Environmental uncertainties require robust control

Evaluation Metrics for Locomotion​

Performance Metrics​

Stability Metrics

  • ZMP tracking error
  • Balance margin maintenance
  • Recovery from disturbances

Efficiency Metrics

  • Energy consumption per unit distance
  • Walking speed achieved
  • Computational resource usage

Robustness Metrics

  • Success rate on various terrains
  • Recovery time from disturbances
  • Adaptability to environmental changes

Summary​

Humanoid robot locomotion is a complex field that combines principles of dynamics, control theory, and biomechanics. Successful locomotion requires careful consideration of gait patterns, footstep planning, and dynamic stability. The choice of walking strategy depends on the specific application, terrain requirements, and robot capabilities. As humanoid robotics continues to advance, new approaches to locomotion will emerge that better approximate human-like movement while maintaining the stability and safety required for practical applications.

Further Reading​

  • McGeer, T. "Passive Dynamic Walking" - Foundational work on dynamic walking
  • Kajita, S., et al. "Biped Walking Pattern Generation by Using Preview Control of Zero-Moment Point" - ZMP-based walking control
  • "Humanoid Robotics: A Reference" by Springer - Comprehensive coverage of locomotion techniques
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