Applications
This is the capstone module where everything comes together. You'll apply vectors, matrices, transformations, eigenvalues, and coordinate frames to solve the core problems of robotics: computing where a robot's hand is, how fast it can move, and how to plan collision-free paths.
What You'll Learn
- Use DH parameters to build kinematic chains for serial robot arms
- Compute end-effector position and orientation via forward kinematics
- Derive and interpret the Jacobian for velocity mapping and singularity analysis
- Evaluate robot dexterity using the manipulability ellipsoid
- Plan paths using potential fields and gradient descent
- Understand configuration space, workspace, and trajectory interpolation
Forward Kinematics
Learn to compute the position and orientation of a robot's end-effector from its joint angles. Master the Denavit-Hartenberg convention and build kinematic chains by multiplying homogeneous transformation matrices.
Velocity Kinematics
Discover how the Jacobian matrix maps joint velocities to end-effector velocities. Understand singularities, the manipulability ellipsoid, and why velocity analysis is essential for real-time robot control.
Path Planning
Apply potential fields, gradient-based planning, and trajectory interpolation to navigate robots through cluttered environments. See how linear algebra underpins every step from configuration space to smooth motion execution.
Prerequisites
- Vector operations (dot product, cross product, projections)
- Matrix multiplication, determinants, and inverses
- Rotation matrices, Euler angles, and homogeneous transforms
- Eigenvalues, coordinate frames, and rotation representations