John M. Hollerbach

Dynamic interactions between limb segments during planar arm movement

Movement of multiple segment limbs requires generation of appropriate joint torques which include terms arising from dynamic interactions among the moving segments as well as from such external forces as gravity. The interaction torques, arising from inertial, centripetal, and Coriolis forces, are not present for single joint movements. The significance of the individual interaction forces during reaching movements in a horizontal plane involving only the shoulder and elbow joints has been assessed for different movement paths and movement speeds. Trajectory formation strategies which simplify the dynamics computation are presented.

A Recursive Lagrangian Formulation of Maniputator Dynamics and a Comparative Study of Dynamics Formulation Complexity

An efficent Lagangian formulation of manipulator dynamics has been developed. The efficiency derives from recurrence relatons for the velocities, accelerations, and generalized forces. The number of additons and multiplicatins varies linearly with the number of joint, as opposed to past Lagrangian dynamics formulations with an n4 dependence. Wih this formulation it should be possible in principle to compute the Lagrangian dynamics in real time. The computational complexities of this and other dynamics formulations including rect Newton-Euler formulations and tabular formulations are compared. It Is concluded that recursive formultions based either on the Lagrangian or Newton-Euler dynamics offer the best method of dynamns calculation.

Redundancy resolution of manipulators through torque optimization

Methods for resolving kinematic redundancies of manipulators by the effect on joint torque are examined. When the generalized inverse is formulated in terms of accelerations and incorporated into the dynamics, the effect of redundancy resolution on joint torque can be directly reflected. One method chooses the joint acceleration null-space vector to minimize joint torque in a least squares sense; when the least squares is weighted by allowable torque range, the joint torques tend to be kept within their limits. Contrasting methods employing only the pseudoinverse with and without weighting by the inertia matrix are presented. The results show an unexpected stability problem during long trajectories for the null-space methods and for the inertia-weighted pseudoinverse method, but more seldom for the unweighted pseudoinverse method. Evidently, a whiplash action develops over time that thrusts the endpoint off the intended path, and extremely high torques are required to overcome these natural movement dynamics.

An oscillation theory of handwriting

Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape. Changing the slope at this zero crossing controls writing slant. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical source; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory.

Time-varying stiffness of human elbow joint during cyclic voluntary movement

SummaryThe objective of this study was to determine the extent to which subjects modulate their elbow joint mechanical properties during ongoing arm movement. Small pseudo-random force disturbances were applied to the wrist with an airjet actuator while subjects executed large (1 rad) elbow joint movements. Using a lumped parameter model of the muscle, tendom and proprioceptive feedback dynamics, a time-varying system identification technique was developed to analyze the phasic changes in the elbow joints mechanical response. The mechanical properties were found to be time-varying, and well approximated by a quasi-linear second-order model. The stiffness of the arm was found to drop during movement. The arm was always underdamped, with the damping ratio changing during movement. Inertia estimates were constant and consistent with previous measurements. Overall, the moving arm was found to be very compliant, with a peak stiffness value less than the lowest value measured during posture, and a natural frequency of less than 3 Hz. Changing the speed of movement, or the load from gravity, changed the stiffness measured, but not in strict proportion to the change in net muscle torque.

Estimation of inertial parameters of manipulator loads and links

The inertial parameters of manipulator rigid-body loads and links have been automatically estimated as a result of gen eral movement. The Newton-Euler equations have been recast to relate linearly the measured joint forces or torques via acceleration-dependent coefficients to the inertial parame ters, which have then been estimated by least squares. Load estimation was implemented on a PUMA 600 robot equipped with an R TI FS-B wrist force-torque sensor and on the MIT Serial Link Direct Drive Arm equipped with a Barry Wright Company Astek wrist force-torque sensor. Good estimates were obtained for load mass and center of mass, and the forces and torques due to movement of the load could be pre dicted accurately. The load moments of inertia were more difficult to estimate. Link estimation was implemented on the MIT Serial Link Direct Drive Arm. A good match was ob tained between joint torques predicted from the estimated parameters and the joint torques estimated from motor cur rents. The match actually proved superior to predicted torques based on link inertial parameters derived by CAD modeling. Restrictions on the identifiability of link inertial parameters due to restricted sensing and movement near the base have been addressed. Implications of estimation accu racy for manipulator dynamics and control have been consid ered.

Dynamic Scaling of Manipulator Trajectories

A fundamental time-scaling property of manipulator dynamics has been identified that allows modification of movement speed without complete dynamics recalculation. By exploiting this property, it can be determined whether a planned trajectory is dynamically realizable given actuator torque limits, and if not, how to modify the trajectory to bring it within dynamic and actuating constraints.

Kinematic stability issues in force control of manipulators

Robots in force control mode often become unstable during contact with stiff environments, due mainly to the high gain nature of wrist force-sensor feedback. Three methods are presented for achieving stable force control compliant coverings or soft sensors, sell-tuning of force gains after estimation of environmental impedance, and reliance on fast open-loop joint torque control and using tip force sensor feedback in a slow loop to maintain accuracy. The latter method is proposed as the best one. Dynamic stability is analysed with a simple model of the robot and its environment. The analyses are verified by single-link experiments on the MIT Serial Link Direct Drive Arm.Robots in force control mode often become unstable during contact with stiff environments, due mainly to the high gain nature of wrist force-sensor feedback. To achieve stable force control, we propose an essential reliance on fast open-loop joint torque control, and relegate tip force sensor feedback to a slow loop to maintain accuracy. Dynamic stability is analyzed with a simple model of the robot and its environment. The analyses are verified by single-link experiments on the MIT Serial Link Direct Drive Arm.

The calibration index and taxonomy for robot kinematic calibration methods

The major approaches toward kinematic calibration are unified by considering an end-point measurement system as forming a joint and closing the kinematic loop. A calibration index is in troduced, based on the mobility equation, that considers sensed and unsensed joints and single and multiple loops and ex presses the surplus of measurements over degrees of freedom at each pose. Past work using open-loop calibration, closed-loop calibration, and screw axis measurement is classified according to this calibration index. Numerical issues are surveyed, in cluding task variable scaling, parameter variable scaling, rank determination, pose selection, and input noise handling.

Deducing planning variables from experimental arm trajectories: Pitfalls and possibilities

This paper investigates whether endpoint Cartesian variables or joint variables better describe the planning of human arm movements. For each of the two sets of planning variables, a coordination strategy of linear interpolation is chosen to generate possible trajectories, which are to be compared against experimental trajectories for best match. Joint interpolation generates curved endpoint trajectories calledN-leaved roses. Endpoint Cartesian interpolation generates curved joint trajectories, which however can be qualitatively characterized by joint reversal points.Though these two sets of planning variables ordinarily lead to distinct predictions under linear interpolation, three situations are pointed out where the two strategies may be confused. One is a straight line through the shoulder, where the joint trajectories are also straight. Another is any trajectory approaching the outer boundary of reach, where the joint rate ratio always appears to be approaching a constant. A third is a generalization to staggered joint interpolation, where endpoint trajectories virtually identical to straight lines can sometimes be produced. In examining two different sets of experiments, it is proposed that staggered joint interpolation is the underlying planning strategy.