AI Robotic Hand --- Fragile Egg Grasping with Tactile Force Control

▶ Open interactive ANITEX · equations and animations

This accessible text edition preserves the document's narrative. See the interactive edition for typeset equations, diagrams and playback.

System Architecture and Scope

Camera → Egg Detection → Pose Estimation → Grasp Planning → Inverse Kinematics → Contact Detection → Force Control → Slip Detection → Force Correction. Tactile normal and tangential force measurements feed back into Force Control, closing the loop. Vision supplies the target pose, not the gripping force. An AI detector could estimate the pose in real hardware; this demonstration uses a known synthetic egg pose and simulated sensors, not a trained vision model or physical robot. The center and bilateral grasp points are marked. A planar two-link arm uses analytic inverse kinematics to reach the gripper wrist. The scene is schematic; its pixels are not calibrated physical dimensions.

Planar Arm Inverse Kinematics

For wrist coordinates (x,y) relative to the base and fixed link lengths L1 and L2: q_2=x^2+y^2-L_1^2-L_2^22L_1L_2, q_1=atan2(y,x)-atan2(L_2 q_2,L_1+L_2 q_2). Forward kinematics recover the wrist position. The displayed arm uses L1=200 and L2=240 scene units with an elbow branch chosen consistently. Collision avoidance, joint limits, orientation control and robot dynamics are outside this simplified model.

Symmetric Grasp Physics

Let m=0.06 kg, g=9.81 m/s squared and nominal friction coefficient mu=0.40. Fn denotes the normal force of each finger, not the sum of both forces. W=mg=0.5886\,N, 2 F_n mg. F_=mg2=0.73575\,N, F_target=S F_=1.25(0.73575)=0.9196875\,N. This is an educational quasi-static friction model. Real shell failure depends on geometry, contact area, materials, defects and egg condition. No force in this document is a certified safe limit for real eggs. Lift acceleration and inertia are neglected; the visual lift is slow and its load remains mg.

Pressure and Soft Tactile Pads

P=F_nA, A P. The nominal area is 100 square millimeters per pad, or 0.0001 square meters. At the initial target, average pressure is about 9.20 kPa. Broad compliant pads distribute load more gently than rigid points. Local peak pressure may exceed this average. The pads are drawn as rounded compliant surfaces; the visual deformation is illustrative, not a shell elasticity calculation.

Slip Detection

Ft is the tangential load per finger. For a symmetrically supported egg, each finger eventually carries mg/2. |F_t| F_n, =|F_t| F_n. Stable: rho below 0.7. Slip Warning: rho from 0.7 up to but not including 0.9. Slip Risk: rho at least 0.9. These conservative thresholds indicate risk, not necessarily actual sliding; the Coulomb bound is rho=1. Calibrate thresholds with real sensors and contact materials. When Fn is zero, the ratio is undefined and the display uses a dash. At 11 seconds the simulated friction coefficient falls from 0.40 to 0.34. This known disturbance drives the slip-risk demonstration; real friction estimation requires calibration and sensing. The normal-force target is corrected to Ft/(mu times 0.65), giving approximately 1.332 N per finger and a stable ratio near 0.65. The original safety factor produces a ratio of 0.8, so the initial hold is a warning, not a stable grasp under these thresholds.

Closed-Loop PID Force Controller

e_F(t)=F_d-F_m, u(t)=K_Pe_F(t)+K_I e_F(t)\,dt+K_Dde_F(t)dt. The output commands the finger actuator. In this simulator u is expressed as an equivalent commanded force rather than motor voltage. Gains are Kp=3, Ki=12 per second and Kd=0.01 seconds. The actuator is a first-order response with time constant 0.18 seconds: dF_mdt=u-F_m0.18. The numerical timestep is 0.02 seconds. Command saturation is 0 to 2.5 N-equivalent. The integral is bounded and conditional integration prevents windup while saturated. Playback seeking reads a precomputed deterministic simulation, so changing playback speed does not change the physics.

State Machine and Safety

APPROACH → CONTACT → FORCE_RAMP → HOLD → SLIP_DETECTION → FORCE_CORRECTION → STABLE_GRASP → LIFT. ANY STATE → SAFETY_RELEASE when measured normal force or average pressure exceeds the illustrative limit. Release is latched until Reset or a scenario change and lifting is aborted. The support table remains under the egg during this example's safety-release event; dropping an unsupported object would not be a generally safe real-world response. Approach lasts 0--3 seconds, contact 3--4, force ramp 4--9, hold 9--11, slip detection 11--13, correction 13--18, stable grasp 18--21 and lift 21--26. These times choreograph the educational sequence. Stable grasp and lifting additionally require rho below 0.7. During ramp the tangential load is progressively applied as a supported proof-load test; the scene does not solve table-contact mechanics. Safety limits are 1.6 N per finger and 20 kPa average pressure. They are illustrative software interlocks, not measured shell-breaking thresholds. Choose the safety-release scenario to command 2.1 N during correction and observe the interlock open the gripper before lifting. Real robots need independent hardware limits and validated emergency procedures.

Interactive Simulation

Play automatically runs the full sequence. Pause and Reset control playback; the timeline inspects individual instants. The graph shows measured and desired normal force, slip ratio, pressure and actuator command. The event log records every state transition. This is a simulation only and sends no commands to hardware.