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Lesson 11.3: Humanoid Robot Control and Balance

Learning Objectives​

After completing this lesson, you will be able to:

  • Understand the principles of humanoid robot balance control
  • Explain the Zero Moment Point (ZMP) concept and its role in stability
  • Analyze feedback mechanisms used in humanoid control systems
  • Design control strategies for stable locomotion
  • Implement basic balance recovery techniques

Introduction​

Humanoid robot control and balance represent one of the most challenging aspects of humanoid robotics. Unlike wheeled or tracked robots, humanoid robots must maintain balance on two legs, making them inherently unstable systems. This lesson explores the fundamental principles of balance control, the mathematical foundations of stability, and the feedback mechanisms that enable humanoid robots to maintain stability during static and dynamic activities.

Fundamentals of Humanoid Balance Control​

The Balance Problem​

Humanoid robots face a unique balance challenge due to their high center of mass and small support base. The key balance problem can be described as:

  • The robot must maintain its center of mass (CoM) within the support polygon defined by its feet
  • External disturbances (pushes, uneven terrain) can cause instability
  • Dynamic motions (walking, running) create additional balance challenges
  • The system is underactuated during flight phases of locomotion

Balance Control Architecture​

Humanoid balance control typically operates on multiple levels:

High-Level Balance Planning

  • Trajectory generation for CoM and ZMP
  • Gait pattern generation
  • Disturbance anticipation and avoidance

Mid-Level Balance Control

  • Whole-body control for coordinated motion
  • Force distribution among contact points
  • Posture adjustment for stability

Low-Level Joint Control

  • Individual joint torque control
  • Motor feedback and safety
  • Real-time stabilization

Zero Moment Point (ZMP) Theory​

Definition and Concept​

The Zero Moment Point (ZMP) is a critical concept in humanoid robotics that defines the point on the ground where the net moment of the ground reaction forces is zero. Mathematically:

ZMP_x = (Σ(Fz_i * x_i) - Σ(M_y_i)) / Σ(Fz_i)
ZMP_y = (Σ(Fz_i * y_i) + Σ(M_x_i)) / Σ(Fz_i)

Where:

  • Fz_i: Vertical force at contact point i
  • x_i, y_i: Position coordinates of contact point i
  • M_x_i, M_y_i: Moments at contact point i

ZMP Stability Criterion​

For a humanoid robot to be stable, the ZMP must remain within the support polygon defined by the feet:

  • Support Polygon: The convex hull of all contact points with the ground
  • Stable Region: Area where ZMP must remain for stability
  • Boundary: Critical for determining when balance is lost

ZMP-Based Control Strategies​

Preview Control

  • Uses future reference trajectories to improve stability
  • Predicts ZMP trajectory and adjusts accordingly
  • Reduces tracking errors and improves robustness

Model-Based Control

  • Uses simplified models like Linear Inverted Pendulum Model (LIPM)
  • Computes desired CoM trajectory to achieve target ZMP
  • Enables real-time balance control

ZMP Feedback Control

  • Measures actual ZMP and compares to desired ZMP
  • Adjusts control inputs to minimize ZMP error
  • Provides robustness to disturbances

Feedback Mechanisms in Humanoid Control​

Sensor-Based Feedback​

Inertial Measurement Units (IMUs)

  • Provide orientation and angular velocity data
  • Critical for balance feedback
  • Used for attitude control and disturbance detection

Force/Torque Sensors

  • Measure ground reaction forces
  • Enable ZMP estimation
  • Provide contact information for gait control

Joint Encoders

  • Provide precise joint position feedback
  • Enable accurate kinematic control
  • Used for motion planning and execution

Control Feedback Loops​

Inner Control Loop (1-10kHz)

  • Joint-level position/velocity/torque control
  • Motor command execution
  • Safety monitoring and limits

Middle Control Loop (100-500Hz)

  • Whole-body control coordination
  • Balance feedback and adjustment
  • Trajectory tracking

Outer Control Loop (10-100Hz)

  • High-level behavior control
  • Task planning and execution
  • Environmental interaction

Feedback Compensation Techniques​

Disturbance Observer

  • Estimates external disturbances
  • Compensates for unmodeled dynamics
  • Improves robustness to environmental changes

Adaptive Control

  • Adjusts control parameters based on system behavior
  • Handles parameter variations over time
  • Improves long-term performance

Stable Locomotion Strategies​

Walking Gait Control​

Static Walking

  • Maintains CoM within support polygon at all times
  • Conservative but stable approach
  • Suitable for initial development and testing

Dynamic Walking

  • Allows CoM to move outside support polygon temporarily
  • More human-like and efficient
  • Requires sophisticated balance control

Gait Phases

  • Double Support: Both feet on ground
  • Single Support: One foot on ground
  • Flight Phase: No feet on ground (running)

Walking Pattern Generation​

Predefined Trajectories

  • Precomputed walking patterns
  • Simple implementation
  • Limited adaptability to disturbances

Online Trajectory Generation

  • Real-time trajectory planning
  • Adaptability to environmental changes
  • Computationally more demanding

Capture Point Control​

The capture point is the location where a robot can come to rest given its current state:

Capture Point = CoM Position + (CoM Velocity / ω)

Where ω = √(g/h), g is gravitational acceleration, and h is CoM height.

Applications of Capture Point Control

  • Balance recovery strategies
  • Gait pattern generation
  • Disturbance response planning

Control Algorithms for Balance​

Linear Quadratic Regulator (LQR)​

LQR provides optimal control for linear systems with quadratic cost functions:

u = -K(x - x_ref)

Where:

  • u: control input
  • K: optimal gain matrix
  • x: system state
  • x_ref: reference state

Advantages

  • Optimal performance for linearized system
  • Systematic design approach
  • Good stability properties

Disadvantages

  • Linearization assumptions may not hold
  • Computationally intensive for high-DOF systems
  • Requires accurate system model

Model Predictive Control (MPC)​

MPC optimizes control inputs over a finite prediction horizon:

min Σ(Cost(x_k, u_k)) for k = 0 to N-1
subject to: x_k+1 = f(x_k, u_k)
            x_k ∈ X, u_k ∈ U

Advantages

  • Handles constraints explicitly
  • Robust to disturbances
  • Can incorporate future predictions

Disadvantages

  • High computational requirements
  • Requires fast optimization solvers
  • Complex tuning

Feedback Linearization​

Transforms nonlinear system into linear system through feedback:

τ = M(q)u + C(q, q̇)q̇ + G(q)

Where u is the new control input that linearizes the system.

Balance Recovery Strategies​

Push Recovery​

When subjected to external pushes, humanoid robots must employ recovery strategies:

Ankle Strategy

  • Use ankle joints to adjust CoM position
  • Suitable for small disturbances
  • Fast response time

Hip Strategy

  • Use hip joints to adjust CoM position
  • Suitable for medium disturbances
  • More movement required

Stepping Strategy

  • Take a step to expand support polygon
  • Suitable for large disturbances
  • Requires dynamic balance control

Recovery Algorithms​

Capture Point-Based Recovery

  • Compute capture point to determine recovery step location
  • Plan step to move capture point to safe region
  • Execute coordinated movement to achieve stability

Model-Based Recovery

  • Use dynamic models to predict recovery trajectories
  • Optimize for minimal energy or time
  • Coordinate multiple joints for recovery

Implementation Considerations​

Real-time Constraints​

Control Frequency Requirements

  • Balance control: 200-1000Hz
  • Whole-body control: 100-200Hz
  • High-level planning: 10-50Hz

Computational Efficiency

  • Simplified models for real-time computation
  • Parallel processing for multiple control loops
  • Approximation algorithms for complex calculations

Safety Considerations​

Fall Prevention

  • Continuous monitoring of stability margins
  • Emergency stop mechanisms
  • Safe fall strategies when recovery fails

Hardware Protection

  • Joint torque limits
  • Velocity and acceleration limits
  • Temperature monitoring

Tuning and Calibration​

Controller Parameters

  • PID gains for joint control
  • Feedback gains for balance control
  • Model parameters for dynamic control

System Identification

  • Estimating robot parameters (mass, inertia)
  • Identifying actuator characteristics
  • Calibrating sensor offsets

Summary​

Humanoid robot control and balance represent complex challenges that require sophisticated control strategies. The Zero Moment Point (ZMP) provides a fundamental framework for stability analysis and control. Multiple feedback mechanisms operating at different frequencies coordinate to maintain balance during static and dynamic activities. Successful implementation requires careful consideration of real-time constraints, safety requirements, and system tuning. As humanoid robotics continues to advance, new control strategies will emerge to enable more robust and human-like balance behaviors.

Further Reading​

  • Kajita, S., et al. "Humanoid Robots: Making Human-like Machines" - Comprehensive treatment of humanoid balance control
  • Pratt, J., & Walking, M. "Virtual Model Control of a Biped Walking Robot" - Advanced control techniques for bipedal robots
  • "Humanoid Robotics: A Reference" by Springer - Detailed reference on control algorithms and implementation
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