Teaching

Learning Objectives

By the end of this course, students will be able to:

• model and analyze the dynamics and control of legged systems with a particular focus on bipeds;

• implement and apply fundamental control concepts for achieving locomotion in legged robots and with powered lower-limb prostheses and exoskeletons; and

• synthesize knowledge from biomechanics, neuroscience, modeling, and control for advanced research in legged mobility or a related role in industry.

Course Schedule

The course progresses from fundamental gait models through body articulation to application domains and is complemented by a final student project.

Introduction

Lecture 1 | Course logistics, legged systems in robotics, observations about legged animals 

Part 1: Fundamental Gait Models

Lectures 2-7 | Stiff, linear, and compliant gaits

1. Stiff Gaits:

• Inverted pendulum, compass walking gait 

• Gait control: passive dynamic walking, active foot placement, active push-off

• Impulsive running, gait transitions

2. Linear Gaits:

• Linear inverted pendulum model, walking capture point

• Gait control: active foot placement, 3-D walking pattern

• Cart-table model, zero moment point, elementary balancing strategies 

• Gait control: ZMP regulation, state space model, LQR, MPC

3. Compliant Gaits:

• Spring-mass model, running and walking

• Gait control: passive dynamic running, active foot placement

• Time-embedding of control in spring mass and compass gait models 

• Gait transitions, multi-legged gaits

Part 2: Body Articulation

Lectures 8-11 | Center body and segmented legs

4. Center Body:

• Physical pendulum, passive and active trunk stability 

• Virtual pivot point, PID control modulated by ground reaction force

• Turning redirection, reorientation, and stability 

• Interference between trunk stability and turning control

5. Segmented Legs:

• Curved feet, walking stability

• Segmented legs in stance (elastic operation, buckling, stabilization strategies)

• Segmented legs in swing (compound pendula, passive dynamics, biarticular control)

• Minimum jerk control

Part 3: Application Domains

Lectures 12-19 | Human system, humanoids, exoskeletons, and prostheses

6. Human System:

• Muscle motors: mechanics, Hill-type models, metabolic cost functions

• Control evidence from neuroscience: CPGs, synergies, sensory organs and reflexes

• Neuromuscular gait models: CPG, lambda, reflexive

• Introduction to modeling human(oid)s using MATLAB SimMechanics

7. Humanoids:

• ZMP walking, Raibert hoppers

• Virtual model control of net wrench

• Centroidal dynamics, resolved momentum and optimization-based control

• Reinforcement learning-based control

8. Exoskeletons and Prostheses:

• Direct amplification

• Motion replay and assist-as-needed control

• Impedance, phase-based, and virtual neuromuscular control

• Human intent integration (targeted reinnervation, myoneural interfaces, deep neural network predictors)

Final Project

Lectures 20-26 | Project implementation and presentations

Students work in groups on a legged mobility problem of their own choosing, synthesizing knowledge and skills from the course.

Learning Resources

The course content primarily draws from research papers. Recommended papers and book sections are posted together with lecture notes.

Programming Tools

Students use MATLAB Simulink for coding challenges in this course, and they are expected to have or acquire sufficient proficiency with this coding environment.  While specific tutorials are not provided, students are encouraged to use available resources including official MathWorks documentation, CMU library resources, and online learning platforms.

Starter code is provided for completing coding challenges. These starters contain essential models and showcase fundamental concepts related to legged systems, and are reviewed as an integral part of the course lectures.

Assessment

Students' comprehension of theoretical concepts and practical application skills are assessed through 4-5 assignments and a final project. The assignments account for 67% of the final grade and typically contain mixed theoretical problems and coding challenges. Example tasks include:

• deriving control for a simple yet fundamental point-mass gait model,

• expanding a provided simulation model of gait to analyze its stability numerically.

The final project accounts for 33% of the final grade. With it, students address a legged mobility problem of their own choosing, allowing them to synthesize the knowledge and skills from the course.