Collaborative Robot Kinematics & Momentum Observer Digital Twin

VIEW PERSPECTIVE 3D

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IK SOLVER DAMPED LEAST SQUARES

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REACH X

X 0.35m

HEIGHT Z

Z 0.45m

Cartesian Target Position

Target X (Reach) 0.45 m

Target Y (Lateral) 0.20 m

Target Z (Height) 0.35 m

Kinematics & Singularity Control

DLS Damping Factor (λ_max) 0.08

Singularity Robustness: When Yoshikawa index w(q) < 0.04 near wrist/shoulder singularity, the Damped Least Squares regularizer dynamically inverts (J J^T + λ² I) to guarantee finite, bounded joint velocities.

ISO/TS 15066 Collision Safety

Sensorless Momentum Observer: Computes generalized momentum p(t) = M(q) q̇ and integrates motor torques to estimate external contact wrench τ̂_ext without expensive 6-axis wrist force-torque sensors or tactile skins.

Real-Time Telemetry

End-Effector [X, Y, Z]	[0.000, 0.000, 0.000] m
Tracking Error	0.0 mm
Manipulability w(q)	0.0000
Observer \|\|τ̂_ext\|\|	0.00 Nm
Active Damping λ	0.0000

1. 6-DOF Anthropomorphic Manipulator Model

2. Damped Least Squares (DLS) Singularity Avoidance

3. Generalized Momentum Observer Collision Detection