Robotics & Physical AI Systems Lab
Explore the fundamental physics, computational geometry, and multi-tier software architectures powering embodied artificial intelligence: from forward and inverse kinematics solvers to actuator torque density sizing, multi-rate control loops, and sim-to-real domain randomization.
Planar Kinematics & Coordinate Transformations
Step through Forward Kinematics (computing end-effector coordinates from joint angles) and numerical Inverse Kinematics via Jacobian Transpose gradient descent. Click or drag anywhere on the workspace to command the arm to track target points in real time.
Actuator Torque Density, Gearbox Physics & Reflected Inertia
Calculate dynamic joint torque, motor phase currents, thermal dissipation ($I^2 R$), and reflected rotor inertia ($J_{rotor} \cdot N^2$) across Quasi-Direct Drive (QDD), Planetary, Cycloidal, and Strain Wave (Harmonic) architectures.
With a 8:1 gear ratio, reflected rotor inertia scales by N² = 64. Low gear ratios preserve backdrivability, allowing the humanoid leg to absorb unexpected ground impacts without stripping gear teeth.
Multi-Rate Control Hierarchy: VLA to Motor Actuation
Physical robots cannot run single monolithic neural control loops. Cognitive Vision-Language-Action (VLA) models evaluate deep vision transformers at 1–5 Hz, generating chunked trajectories. Mid-level planners interpolate at 20–50 Hz, while Field-Oriented Control (FOC) joint loops run at 200–1000 Hz.
Sim-to-Real Domain Randomization Sandbox
Examine how learned physical neural policies perform when deployed from idealized simulations (MuJoCo/Isaac Sim) into the real world. Adjust friction variation, unmodeled mass perturbations, and communication latency to evaluate trajectory divergence.