* 16-868

H Geyer Image

16-868 Biomechanics and Motor Control

Recommended Books

[A03]  Principles of Animal Locomotion
R McN Alexander, 2003.

[W09]  Biomechanics and Motor Control of Human Movement
DA Winter, 2009.

[M84]  Muscles, Reflexes and Locomotion
TA McMahon, 1984.

[E08]  Neuromechanics of Human Movement
R Enoka, 2008.

[R86]  Legged Robots that Balance
M Raibert, 1986.

Assignments and Projects

Assignments will determine 50% of your grade. They will be handed out about every two weeks and consist of mixed problems in theory and implementation in Matlab Simulink/SimMechanics. The deadline for submission is at midnight on the due date. Please submit your assignments as pdf and commented code.  Assignments can be downloaded and uploaded through CMU Blackboard.

Projects will determine the other 50% of your grade. The projects ideally help you with your research. Team projects are highly encouraged. Projects include a presentation talk during the last week of lectures and a final technical report that is due one week later.

Syllabus and Resources


1 Basic Observations about Legged Animals 
Gait Analysis Methods
Morphology of Legged Animals
Gaits and Energy Efficiency
Common Stance Dynamics

Variety of gaits
Gaits and energy economy

2 Standing  [W09]
Inverted Pendulum Model (IPM)
Ankle Strategy, COP, ZMP and Polygon of Support
Hip Strategy and Flywheel Extension
Stepping Strategy and Linear Inverted Pendulum Model (LIPM)
Capture Points in 2D
Bilateral Leg Loading

Review of human balance strategies
LIPM capture points and flywheel extension

3 Walking [A03,E08,M84]
Inverted Pendulum Stance
Impacts in Legged Locomotion
Dynamic Walking Speed Limit
Double Pendulum Swing
Passive Dynamic Walkers and Stability
Active Dynamic Stability in 2D and 3D (LIPM)

Impact losses in human experiments
Comparison of theoretical speed limit with human walk-run transition
Ballistic swing model and human swing times
Passive dynamic walker
Passive dynamic stability
Active walking stability using linear inverted pendulum model

4 Running [A03,E08,M84,R86]
Spring-Mass Model (SMM)
Dynamic Similarity of Running Animals
Mechanical Self-Stability
Active Dynamic Stability in 2D and 3D
Raibert Controller

Spring-mass model
Dimensionless leg stiffness of animals
Self-stable running model
Active running stability using spring mass model

5 Integrated Gait Models
Load Sharing in Double Support of Walking
Bipedal Spring Mass Model (BSMM)
Lack of Control Unification

Load sharing in walking horses
Bipedal spring mass model


6 Muscle Motors [M84,A03,E08]
Muscle Tendon Units
Activation Dynamics
Force-Length and Force-Velocity Relationships
Hill-type Muscle Models
Muscle Metabolic Power
Dynamics of Electric Motor Units
Series Elastic and Variable Impedance Actuators

Hill-type muscle modeling
Parallel elasticity arrangement
Metabolic rate of human muscle and its functional representation
Series elastic actuators

7 Observations about Motor Control [E08]
Muscle Motor Patterns in Legged Locomotion
Evidence for Central Pattern Generators (CPGs)
Evidence for Sprinal Reflex Control
Current View on CPG vs Reflex Control

Human motor patterns in walking and running
Brown's original paper on central pattern generation
Review of CPG control
Signal content of muscle spindles and GTOs
Summary of Sherrington's work on reflex control
H-reflex as method to probe spinal circuitry

8 Human Control Models of Locomotion
Neuron Model and Matzuoka Oscillator
Taga's Basic Locomotion Model using CPGs
Hase's 3D Extension
Reflex Control of Stance Leg Behavior
Reflexive Walking and Running

Neuron and oscillator model
Taga's original CPG-based locomotion model
Extension to 3D locomotion
Positive force feedback for load bearing and compliant leg behavior
Reflexive walking model
Extension to 3D and running

9 Comparison to Humanoid Controllers
Equations of Motion of Humanoid Systems
Virtual Model Control via Jacobian Mapping
Zero Moment Point (ZMP) and Reference Trajectory Control
Behavior Optimization and Reference Torque Control

Virtual model control of walking robots Preview control using LIPM for ZMP-based trajectory control model-predictive control of humanoids

Accompanying Computer Labs


Basic Modeling of Dynamical Systems with Simulink (1 Lab)
Models as Signal Flows from Sources to Sinks
Integration of Equations of Motion
Vertical Spring Mass Model of Bouncing Dynamics
Interaction with Matlab Scripts

Solving EOMs using SimMechanics (Standing, 1)
Solving EOMs of Kinematic Chains with SimMechanics
Inverted Pendulum Stance Model
Ankle Strategy and Polygon of Support
*Hip Strategy and Flywheel Extension

Implementation of Point-Mass Gait Models (Walking, 2)
Separation of Integration and Leg Force Computation
Inverted Pendulum Stance Forces
Phase Switching Between Stance and Swing
Inverted Pendulum Walking
Animations within Simulink
Push-off and Capture Points
Linear Inverted Pendulum Walking Model
*Active Dynamic Stability in 3D

Analysis of Point-Mass Gait Models (Running, 1)
Spring-Mass Model Implementation
Automated Generation of System Behavior Tables
Active Running Stability

Explicit Modeling of Contact Dynamics (1)
Models of Contact Dynamics
Implementation with Body Actuators in SimMechanics
*Raibert Hopper and Control

Survey of contact dynamics modelling


Dynamics of Muscle Tendon Units (Muscle Motors, 1)
Representation of Excitation Contraction Coupling
Testing Force-Length and Force-Velocity Relationships
Implementation of Hill-type Muscle Models via Integration
*Quick Release Experiment

Dynamics of Series Elastic Actuators (Muscle Motors, 1)
Implementation of Series Elastic Actuator Models
Control Strategies based on Torque, Velocity and Position

Basic Neuromuscular Modeling in Simulink (Human Control, 1)
Modeling Muscle-Segment Attachment
Hopping Model
Spinal Reflex Implementation
*Positive Force Feedback Control of Compliant Leg Behavior

Neuromuscular Systems in SimMechanics (Human Control, 3)
Implementation of Matzuoka Rhythm Generator
Implementation of Taga’s Locomotion Model

� H. Geyer, 7 Sep 2012