Advanced Control and Robotics Studies

Hybrid dynamics, constrained optimization, and trajectory optimization studies

Overview

This project consolidates several advanced simulation-based studies in nonlinear control, hybrid locomotion modeling, constrained inverse kinematics, and trajectory optimization.

Each study focuses on mathematical modeling, numerical implementation, and simulation-based validation.

1. Hybrid Locomotion Modeling – ALIP

Implementation and study of the Angular Momentum Linear Inverted Pendulum (ALIP) model for step-to-step locomotion analysis.

This implementation replicates and analyzes the reduced-order locomotion framework presented by Y. Gong and J. W. Grizzle in their work on zero dynamics and angular momentum in bipedal locomotion.

Technical Highlights

  • Closed-form discrete dynamics
  • Hybrid reset map
  • Momentum-based foot placement control
  • Velocity tracking across multiple steps
  • 2D animated walking simulation
  • Reference *

Gong, Y., & Grizzle, J. W.
Zero Dynamics, Pendulum Models, and Angular Momentum in Feedback Control of Bipedal Locomotion.

2. Constrained Inverse Kinematics – Robotic Arm

Two optimization-based IK formulations were implemented.

IK via Quadratic Programming (IK-QP)

  • Linearized differential kinematics
  • QP formulation with constraints
  • Regularization and smooth motion

IK via Nonlinear Programming (IK-NLP)

  • Full nonlinear optimization
  • Obstacle avoidance constraint
  • End-effector trajectory shaping

3. Trajectory Optimization – Direct Collocation

Implementation and numerical study of trajectory optimization using direct collocation methods.

The formulation, discretization, and nonlinear programming structure were replicated from the tutorial developed by Matthew Kelly.

Features

  • Discretized nonlinear dynamics
  • Equality constraints for system evolution
  • Nonlinear programming formulation
  • Numerical optimal control solution
  • Reference *

Kelly, M.
An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation.
https://www.matthewpeterkelly.com/tutorials/trajectoryOptimization/index.html

4. Multibody Simulation – Self-Balancing Robot

Dynamic modeling and PID control of a self-balancing robot.

Implemented in

  • ODE45 simulation
  • Simscape Multibody

Technical Focus

  • Hybrid dynamical systems
  • Reduced-order locomotion models
  • Constrained optimization
  • Quadratic programming
  • Nonlinear programming
  • Trajectory optimization
  • Multibody simulation

Repository

The complete source code for all studies is available on GitHub:

Advanced Control and Robotics Studies