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Your contribution supports educational open-source robotics simulators, student laboratories, and WebGL computational research.
A real-time WebGL robotics simulation cockpit built for forward & inverse kinematics, Denavit-Hartenberg parameters, Levenberg-Marquardt Damped Least Squares (DLS) & CCD solvers, Yoshikawa manipulability dexterity analysis, and LSPB trajectory velocity profiling.
NEXUS bridges high-level robot control with rigorous classical robotics mechanics: matrix kinematics, analytical differential geometry, and numerical optimization.
Evaluates the geometric velocity Jacobian $\mathbf{J}_v = \mathbf{z}_i \times (\mathbf{p}_e - \mathbf{p}_i)$ and computes the Yoshikawa Manipulability index $w = \sqrt{\det(\mathbf{J}\mathbf{J}^T)}$ to predict singularities and kinematic locking.
YOSHIKAWA DEXTERITYCompare Levenberg-Marquardt Damped Least Squares ($\mathbf{J}^T(\mathbf{J}\mathbf{J}^T + \lambda^2 \mathbf{I})^{-1}$) against Singularity-Damped Cyclic Coordinate Descent (CCD) for ultra-fast sub-millisecond cartesian convergence.
SUB-1.2MS CONVERGENCEGenerates continuous linear segment motions with parabolic blend transitions (LSPB), ensuring zero acceleration discontinuity, bounded actuator jerk, and configurable blend durations $t_b$.
C1-CONTINUOUS MOTIONReal-time estimation of joint gravity torques $\mathbf{g}(\mathbf{q})$, centrifugal/Coriolis forces, and payload capacities per axis to visualize dynamic motor thermal limits.
NEWTON-EULER MOMENTSNEXUS allows you to dynamically reconfigure the simulator from a planar 2-link pedagogical arm to a full 6-DOF industrial anthropomorphic manipulator.
Pedagogical 2-revolute joint arm. Ideal for mastering analytical inverse kinematics equations, geometric circle intersections, and 2D reachability circles.
3-joint arm introducing waist yaw rotation and shoulder/elbow pitch. Maps out full 3D spatial hemispheres and Cartesian coordinate transformations.
High-speed pick-and-place configuration with compliant horizontal revolute joints and rigid vertical prismatic quill axis for PCB assembly.
Full 6-DOF industrial manipulator with spherical wrist. Complete position $(X, Y, Z)$ and orientation $(\phi, \theta, \psi)$ dexterity in 3D Euclidean space.
Summary of mathematical algorithms, performance benchmarks, and browser runtime capabilities.
| SUBSYSTEM | IMPLEMENTATION | SPECIFICATION DETAILS |
|---|---|---|
| 3D Graphics Engine | Three.js WebGL (r128 / r183) | Directional lighting, coordinate axis frames, joint rings, shadow mapping, 60 FPS |
| Kinematics Paradigm | Standard Denavit-Hartenberg (DH) | Homogeneous transformation matrices $\mathbf{T}_i^{i-1}(\theta, d, a, \alpha)$ for arbitrary N-link chains |
| Inverse Kinematics | DLS (Levenberg-Marquardt) + CCD | Singularity-damped least squares with numerical stability guarantees near singular boundaries |
| Manipulability Metric | Yoshikawa Index $w = \sqrt{\det(\mathbf{J}\mathbf{J}^T)}$ | Real-time condition number $\kappa(\mathbf{J})$ and singular value decomposition (SVD) velocity ellipsoid |
| Trajectory Generation | LSPB (Linear with Parabolic Blend) | Continuously differentiable velocities with configurable blend duration $t_b$ and acceleration limits |
| Dynamics & Torques | Dynamic Gravity Compensation | Live multi-axis torque estimation taking into account link masses and payload leverage arms |
| Zero Dependencies | Pure Vanilla ES Modules | Zero backend; runs client-side inside modern WebGL browsers at native refresh rate |
Your contribution supports educational open-source robotics simulators, student laboratories, and WebGL computational research.