Ara Arabyan

An Improved Formulation for Constrained Mechanical Systems

This paper presents an investigation of the advantages of a new formulation in the study of mechanical systems with holonomic and nonholonomic constraints. The formulation, originally proposed for systems of constrained particles, provides an efficient and robust means of simulating general multibody systems in the presence of redundant, degenerate and intermittent constraints. The structure of the formulation also allows the use of a dynamics code for pure kinematics analysis with a simple substitution. In addition, the formulation separates applied and constraint forces explicitly allowing recovery of constraint forces by straightforward means. Several examples are given to demonstrate the effectiveness of the formulation in special circumstances.

A DISTRIBUTED CONTROL MODEL FOR THE AIR-RIGHTING REFLEX OF A CAT

Abstract. A multisegment, multijoint model of a falling animal is presented to examine the effectiveness of a two-stage control scheme in a zero-momentum self-righting maneuver. The model contains a much larger number of degrees of freedom than is required to execute a self-righting maneuver and is thus capable of providing multiple solutions for the same task. The decentralized control scheme is designed to achieve gross turning in minimum time and to maintain a steady orientation relative to gravity after the turn has been achieved. The scheme is able to determine the sequence of steps necessary to execute the motor task and also incorporates learning features. Results from various simulations are presented and their implications discussed.

Modeling of control and learning in a stepping motion

In a previous study (Beuter et al. 1986) the authors modeled a stepping motion using a three-body linkage with four degrees of freedom. Stepping was simulated by using three task parameters (i.e., step height, length, and duration) and sinusoidal joint angular velocity profiles. The results supported the concept of a hierarchical control structure with open-loop control during normal operation. In this study we refine the dynamic model and improve the simulation technique by incorporating the dynamics of the leg after landing, adding a foot segment to the model, and preprogramming the complete step motion using cycloids. The equations of the forces and torques developed on the ground by the foot during the landing phase are derived using the Lagrangian method. Simulation results are compared to experimental data collected on a subject stepping four times over an obstacle using a Selspot motion analysis system. A hierarchical control model that incorporates a learning process is proposed. The model allows an efficient combination of open and closed loop control strategies and involves hardwired movement segments. We also test the hypothesis of cycloidal velocity profiles in the joint programs against experimental data using a novel curve-fitting procedure based on analytical rather than numerical differentiation. The results suggest multiob-jective optimization of the joints motion. The control and learning model proposed here will help the understanding of the mechanisms responsible for assembling selected movement segments into goaldirected movement sequences in humans.

Fitting mathematical functions to joint kinematics during stepping: Implications for motor control

The present study extends past work on modeling and control of stepping. The relationship between joint space kinematic data and routine motor control (i.e., open loop) during human stepping is investigated. A model of open loop stepping control using joint kinematics is described. Different functional approximations are employed to simulate experimental joint kinematic data collected on a subject stepping repeatedly over an obstacle. Results indicate that joint kinematics can be characterized by a small number of functions yielding a simple analytical description of open loop motor control. The different basis functions used and their associated coefficients reflected the qualitative behavior of joint trajectories thus allowing flexibility in the formulation of system kinematics. This approach provides a tool to study movement pathologies and movement development by identifying the basis functions governing the kinematics of motion and their associated coefficients. The model presented here is helpful in studying the segmentation of multiarticular movements into their elementary components by analytically modeling the discrete organization of motor behavior.

Directional effects of changes in muscle torques on initial path during simulated reaching movements

Abstract Adults are able to reach for an object for the first time with appropriate direction, speed, and accuracy. The rules by which the nervous system is able to set muscle activities to accomplish these outcomes are still debated and, indeed, the sensitivity of kinematics to variations in muscle torques is unknown for complex arm movements. As a result, this study used computer simulations to characterize the effects of change in muscle torque on initial hand path. The same change was applied to movements towards 12 directions in the horizontal plane, and changes were systematically manipulated such that: (1) torque amplitude was changed at one joint, (2) timing of torque was changed at one joint, and (3) amplitude and/or timing was changed at two joints. Results showed that simultaneous changes in torque amplitude at shoulder and elbow joints affected initial speed uniformly across direction. These results add to conclusions from previous experimental and modeling work that the simplest rule to produce a desired change in speed for any direction is to scale torque amplitude at both joints. In contrast, all simulations showed nonuniform effects on initial path direction. For some regions of the workspace, initial path direction was little affected by either a ±30% change in amplitude or a ±100-ms change in timing, whereas for other regions the same changes produced large effects on initial path direction. These findings suggest that the range of possible torque solutions to achieve a particular initial path direction varies within the workspace and, consequently, the requirements for an accurate initial path will vary within the workspace.

H/sub /spl infin//-optimal mapping of actuators and sensors in flexible structures

A computationally efficient method is described to search and find optimal spatial configurations for the placement (mapping) of a finite number of actuators and sensors on a continuous flexible structure to reduce the vibrations or deformations in the structure to a minimum in the H/sub /spl infin// sense. The method produces a feedback controller corresponding to the minimal H/sub /spl infin// norm of the disturbance-deformation operator. The computational cost of the optimal mapping search is reduced through two techniques. First, the computationally expensive goal function based on the complete H/sub /spl infin// synthesis is evaluated only for the mappings that pass a computationally inexpensive test. Next, the target norm is adjusted statistically based on the already evaluated mappings. Mapping optimization based on exhaustive search and genetic algorithms are presented and demonstrated on a 30-node finite-element model of a simply supported beam.

Phase plane modeling of leg motion

Phase plane analysis of dynamical systems, in which variables are plotted against their time derivatives, has been recently emphasized as a general method for reconstructing system dynamics from data. The purpose of this experiment was to develop a model of leg movement in a stepping task using the phase plane approach. In this model, the leg is represented as a three-body linkage and the motion of the leg is assumed to be planar with four degrees of freedom. Experimental data was collected on one subject stepping six times, using a two dimensional videomotion analysis system with reflective markers placed on the lower limb joints. A computer program able to solve the equations of motion and compute the state of the system for a given task was implemented. This computer program was written to generate the motion of the leg for a given task using inverse kinematics and a preplanned foot path. Foot trajectories with cycloidal, constant acceleration/deceleration and sinusoidal velocity profiles were studied. From the results, an attempt was made to identify the variables which are measured and to determine the motion characteristics during stepping. The preliminary results support the concept of a hierarchical control structure with openloop control during normal operation. During routine activity there is no direct intervention of the Central Nervous System (CNS). The results support the existence of preprogramming and provide a starting point for the study of the development of control in multiarticulate movements.

A novel approach to the dynamic analysis of highly deformable bodies

A method using element-fixed moving reference frames is introduced to compute the behavior of highly deformable bodies undergoing large and fast rotations. The use of reference frames attached to each finite element allows the correct computation of overall large deformations and the characterization of rigid-flexible coordinate coupling through the systematic incorporation of higher-order kinematic terms and time derivatives of coordinate transformation matrices. The approach is applied to planar rotating Bernoulli beams of various flexural rigidities and the results are compared to those obtained by other methods and ABAQUS, a nonlinear finite element package. The results indicate excellent agreement with published data and superior efficiency of computation.

Limits of vibration suppression in flexible structures

A method is described for the determination of limits of vibration suppression in an elastic structure by means of a given number of control actuators. The method is based on a theorem, described and proved herein, that defines the lower limit of residual deformations for specified disturbances and a given map of placement of actuators which can produce finite control forces. The new method can identify regions of placement which result in acceptable residual deformations, thus making control design easier and reduces the cost of searching for optimal actuator positions. Unlike traditional methods used to solve this class of problems, the new method does not require knowledge about the excitation states of various deformation modes. The method is demonstrated by applying it to a simply supported beam and a plate.

Lower limits of deformation suppression in flexible structures

Based on the four-block formulation of the active deformation suppression problem, the concepts of actual and optimistic lower limits of deformation suppression in terms of the H/sup /spl infin// norm have been introduced for flexible structures for limited numbers of actuators and sensors. These limits have been used to construct a hybrid search algorithm for actuator and sensor mapping optimization, resulting in significant gains in computational costs. A simply supported beam control has been used as a numerical testbed, to demonstrate the acclaimed properties of the lower limits of deformation suppression.