Humanoid Arm Control: Math Modeling for Kinematics, Trajectory Planning, and Joint Control
Master the art of humanoid arm control through mathematical modeling, kinematics, trajectory planning, and joint control techniques.
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Introduction to Humanoid Arm Kinematics
Unit 1: Humanoid Arm Anatomy and Degrees of Freedom
Anatomy of a Hum. Arm
Degrees of Freedom (DoF)
Workspace & Dexterity
Joint Space vs. Cartesian
End-Effector Defined
Unit 2: Forward and Inverse Kinematics Concepts
What is Kinematics?
Forward Kinematics Intro
Inverse Kinematics Intro
Applications of Kinematics
Kinematics: A Simple Example
Unit 3: Introduction to Denavit-Hartenberg (DH) Convention
Why DH Convention?
DH Parameters Overview
Coordinate Frames
DH Table
DH Convention Summary
Denavit-Hartenberg (DH) Parameter Formulation
Unit 1: Understanding the DH Convention
Intro to DH Convention
DH: Coordinate Frames
Common Mistakes
Visualizing DH Frames
Practice: Simple Arm
Unit 2: Determining DH Parameters
Link Length (a_i)
Link Twist (alpha_i)
Joint Offset (d_i)
Joint Angle (theta_i)
Putting it Together
Unit 3: Creating and Interpreting DH Tables
DH Table Structure
Example DH Table
Table for your Arm
Interpreting the Table
DH Table Pitfalls
Forward Kinematics
Unit 1: Homogeneous Transformation Matrices
Intro to Transformations
Rotation About X-axis
Rotation About Y-axis
Rotation About Z-axis
Translation in 3D Space
Unit 2: Forward Kinematics Calculation
Transformation Composition
DH to Transformation Matrix
From Base to End-Effector
End-Effector Position
End-Effector Orientation
Unit 3: Forward Kinematics Implementation
Python Setup
DH Parameters in Code
Transformation Function
Forward Kinematics Code
Visualization
Inverse Kinematics: Analytical Solutions
Unit 1: Understanding Inverse Kinematics
What is IK?
Challenges of IK
Redundancy in IK
Analytical vs. Numerical
When to Use Analytical
Unit 2: 2-DOF Planar Arm IK
2-DOF Arm Overview
Geometric IK Solution
Multiple Solutions
Singularities
Coding the 2-DOF IK
Unit 3: 3-DOF Planar Arm IK
3-DOF Arm Overview
Solving 3-DOF IK
Elbow Up/Elbow Down
3-DOF Singularities
Coding 3-DOF IK
Trajectory Planning in Joint Space
Unit 1: Introduction to Trajectory Planning
What is Trajectory?
Joint Space vs. Task Space
Key Considerations
Trajectory Planning Steps
Unit 2: Linear Trajectory Planning
Linear Trajectories
Linear Trajectory Equations
Implementation
Pros and Cons
Unit 3: Polynomial Trajectory Planning
Polynomial Trajectories
Cubic Polynomials
Quintic Polynomials
Implementation
Pros and Cons
Unit 4: Advanced Trajectory Planning Concepts
Via Points
Trajectory Scaling
Joint-Level Control with PD Controllers
Unit 1: Introduction to Feedback Control
Why Use Feedback?
Components of Feedback
Error Signals
Joint Control Overview
Stability in Control
Unit 2: PD Controller Design and Implementation
Proportional Control
Derivative Control
Putting it Together: PD
Simulating a PD Controller
Code: PD Controller
Unit 3: Tuning and Performance Evaluation
Tuning Kp
Tuning Kd
Tuning Strategies
Performance Metrics
Dealing with Limits
Sensor Integration and Error Correction
Unit 1: Introduction to Sensor Integration
The Role of Sensors
Joint Encoders
Simulating Joint Encoders
Data Acquisition
Unit 2: Integrating Sensor Data into the Control Loop
Feedback Control
PD Control with Feedback
Tuning with Sensor Data
Simulation Refinement
Unit 3: Error Correction Strategies
Sensor Calibration
Filtering Techniques
Observer Design
Fault Detection
Adaptive Control
Unit 4: Advanced Topics
Sensor Fusion
Real-Time Implementation
Recap & Next Steps