Matt Strong

Matt Strong

CS PhD at Stanford University

← Paper Digest

Articulated Hands: Force Control and Kinematic Issues

J. Kenneth Salisbury, John J. Craig

Seminal March 1982 · The International Journal of Robotics Research

TL;DR Kinematic and control design of the three-finger, 9-DOF Stanford-JPL hand. A mobility analysis picks the finger layout (39 of 600 candidate designs pass), isotropic points mark where fingertip forces are most accurate, and a Cartesian hand controller sets object stiffness and internal grasp forces without inverse kinematics.

What they do

Salisbury and Craig work through the kinematic and control design of the Stanford-JPL hand: three fingers with three joints each. Motors sit on the forearm and drive each finger through four Teflon-coated cables in flexible conduit. A cantilever beam and idler pulley sense each cable’s tension where it enters the finger, so the tension loop encloses motor, gear and conduit friction.

How it works

  • Mobility analysis. A modified Grübler formula gives the connectivity between palm and object. A design must reach C = 6 with joints free and C’ ≤ 0 with joints locked (object fully constrained). They enumerate 600 three-finger, three-link designs.
  • Isotropic points. The condition number of the transposed Jacobian bounds how torque errors become fingertip-force errors. Where it equals 1, force accuracy is best and joint noise spreads equally in all directions. Fingers are placed so their circular loci of such points touch a nominal 1-inch sphere.
  • OPHAND. Gradient-free conjugate-direction search (Powell 1964) over subsets of a 36-parameter hand model, scoring the volume reachable by a fingertip-grasped object.
  • Control. Each tendon has feedforward plus a constant-gain regulator with an integral term; a bearing force is chosen to keep all tensions positive. A 9×9 grasp matrix, inverted once per grasp, maps object stiffness and three internal grasp forces to fingertip commands, with no inverse kinematics or inverse Jacobian.

Results

  • 39 of 600 designs pass. The 33 with frictionless five-DOF contacts are rejected because they cannot apply moments to cylinders or spheres. The chosen 4-4-4 design (point contact with friction) is the only one where extra joints tighten the grasp (C’ = −3).
  • A two-link parallel-axis finger with a = 0.707 has a true isotropic point.
  • OPHAND’s thumb placement more than doubled the performance index of the original heuristic design.
  • A prototype tendon-driven joint is shown following torque steps against a stiff aluminum-on-steel environment; no error numbers are given.

Limitations

Only that one joint was tested; the hand controller was not yet implemented. OPHAND scores only fingertip grasps, the design enumeration assumes one contact type for all contacts, and the grasp matrix assumes fixed grasp points.

Figures

From Figure 8: Top and side views of the Stanford-JPL hand, with the thumb placement found by OPHAND.
From Figure 8: Top and side views of the Stanford-JPL hand, with the thumb placement found by OPHAND.
From Figure 3: The eight ways a three-link finger can touch an object, combined across fingers to enumerate candidate...
From Figure 3: The eight ways a three-link finger can touch an object, combined across fingers to enumerate candidate hand designs.
From Figure 5: Condition number of the force transform across the workspace of two-link fingers with parallel revolut...
From Figure 5: Condition number of the force transform across the workspace of two-link fingers with parallel revolute joints. Only the a = 0.707 design reaches the isotropic value of 1.
From Figure 13: Cartesian hand controller. Fingertip position and velocity errors pass through grasp-matrix stiffness...
From Figure 13: Cartesian hand controller. Fingertip position and velocity errors pass through grasp-matrix stiffness and damping blocks, are added to the desired force and are sent to the three finger controllers.
Abstract

Kinematic and control issues are discussed in the context of an articulated, multifinger mechanical hand. Hand designs with particular mobility properties are illustrated, and a definition of accuracy points within manipulator workspace is given. Optimization of the physical dimensions of the Stanford-JPL hand is described. Several architectures for position and force control of this multiloop mechanism are described, including a way of dealing with the internal forces inherent in such systems. Preliminary results are shown for the joint torque subsystem used in the hand controller.

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