Karim Abdel-Malek

Geometric representation of the swept volume using Jacobian rank-deficiency conditions

A broadly applicable formulation for representing the boundary of swept geometric entities is presented. Geometric entities of multiple parameters are considered. A constraint function is defined as one entity is swept along another. Boundaries in terms of inequality constraints imposed on each entity are considered which gives rise to an ability of modeling complex solids. A rank-deficiency condition is imposed on the constraint Jacobian of the sweep to determine singular sets. Because of the generality of the rank-deficiency condition, the formulation is applicable to entities of any dimension. The boundary to the resulting swept volume, in terms of enveloping surfaces, is generated by substituting the resulting singularities into the constraint equation. Singular entities (hyperentities) are then intersected to determine sub-entities that may exist on the boundary of the generated swept volume. Physical behavior of singular entities is discussed. A perturbation method is used to identify the boundary envelope. Numerical examples illustrating this formulation are presented. Applications to NC part geometry verification, robotic manipulators, and computer modeling are discussed.

Multi-objective Optimization for Upper Body Posture Prediction

*† ‡ § ** The demand for realistic autonomous virtual humans is increasing, with potential application to prototype design and analysis for a reduction in design cycle time and cost. In addition, virtual humans that function independently, without input from a user or a database of animations, provide a convenient tool for biomechanical studies. However, development of such avatars is limited. In this paper, we capitalize on the advantages of optimization-based posture prediction for virtual humans. We extend this approach by incorporating multi-objective optimization (MOO) in two capacities. First, the objective sum and lexicographic approaches for MOO are used to develop new human performance measures that govern how an avatar moves. Each measure is based on a different concept with different potential applications. Secondly, the objective sum, the min-max, and the global criterion methods are used as different means to combine these performance measures. It is found that although using MOO to combine the performance measures generally provides reasonable results especially with a target point located behind the avatar, there is no significant difference between the results obtained with different MOO methods.

Towards a new generation of virtual humans

This paper presents work from an ongoing project towards developing a new generation of virtual human models that are highly realistic in appearance, movement, and feedback. Santos™, an anatomically correct human model with more than 100 degrees of freedom, is an avatar that exhibits extensive modelling and simulation capabilities, resides in a virtual environment, and conducts human-factors analysis. The paper presents an optimisation-based approach to posture and motion prediction that allows the avatar to operate with autonomy rather than depending on stored animations and data or being restricted by inverse kinematics. It also presents approaches to determining reach envelopes and workspace zone differentiation, and discusses methods for evaluating the physiological status of the virtual human as it completes tasks. Muscle modelling including muscle wrapping, muscle force and stress determination is also discussed. Finally, the process of building a 25-DOF hand model is described. The result is an exciting step towards a virtual human that is more extensive and complete than any other.

Towards understanding the workspace of human limbs

Significant attention in recent years has been given towards obtaining a better understanding of human joint ranges, measurement, and functionality, especially in conjunction with commands issued by the central nervous system. Studies of those commands often include computer algorithms to describe path trajectories. These are typically in ‘open-form’ with specific descriptions of motions, but not ‘closed form’ mathematical solutions of the full range of possibilities. This paper proposes a rigorous ‘closed form’ kinematic formulation to model human limbs, understand their workspace (also called the reach envelope), and delineate barriers therein where a path becomes difficult or impossible owing to physical constraints. The novel ability to visualize barriers in the workspace emphasizes the power of these closed form equations. Moreover, this formulation takes into account joint limits in terms of ranges of motion and identifies barriers therein where a person is required to attain a different posture. Examples include the workspaces of a typical forearm and a typical finger. The wrists range of motion is used to illustrate the visualization of the progress in the functionality of a wrist undergoing rehabilitation.

A new digital human environment and assessment of vehicle interior design

Vehicle interior design directly relates to driver performance measures such as comfort, efficiency, risk of injury, and vehicle safety. A digital human is a convenient tool for satisfying the need to reduce the design cycle in order to save time and money. This paper presents a digital human environment, Santos(TM), developed at The University of Iowa, and its assessment as applied to the interior design of a Caterpillar vehicle. The digital human environment involves male models and accommodates a large percentage of the operator population (from the 5th percentile to the 95th percentile). It has a user-friendly interface and includes various tools such as posture prediction, reachability check, zone differentiation, and biomechanics assessment for the upper body and hand. The key difference from a traditional digital human environment is that Santoss environment is optimization-based. This can answer design questions regarding whether the operator can reach relevant controls, what the comfort level is if one can reach the control, and what strength is required of the operator to pull a shift, etc. The illustrative example of a Caterpillar cab is demonstrated using this digital human environment.

A New Discomfort Function for Optimization-Based Posture Prediction

Using multi-objective optimization, we develop a new human performance measure for direct optimizationbased posture prediction that incorporates three key factors associated with musculoskeletal discomfort: 1) the tendency to move different segments of the body sequentially, 2) the tendency to gravitate to a comfortable neutral position, and 3) the discomfort associated with moving while joints are near their respective limits. This performance measure operates in real-time and provides realistic postures. The results are viewed using Santos TM , an advanced virtual human, and they are validated using motion-capture. This research lays groundwork for studying how and why humans move as they do.

Optimization-based prediction of asymmetric human gait

An optimization-based formulation and solution method are presented to predict asymmetric human gait for a large-scale skeletal model. Predictive dynamics approach is used in which both the joint angles and joint torques are treated as unknowns in the equations of motion. For the optimization formulation, the joint angle profiles are treated as the primary unknowns, and velocities and accelerations are calculated using them. In numerical implementation, the joint angle profiles are discretized using the B-spline interpolation. An algorithm is presented to inversely calculate the joint torques and the ground reaction forces. The sum of the joint-torques squared, called the dynamic effort, is minimized as the human performance measure. Constraints are imposed on the joint strengths (torques) and joint ranges of motion along with other physical constraints. The formulation is validated by simulating a symmetric gait and comparing the results with the experimental data. Then asymmetric gait motion is simulated, where the left and right step lengths are different. The kinematics and kinetics results from the simulation are presented and discussed. Predicted ground reaction forces are explained by using the inverted pendulum model. Predicted kinematics and kinetics have trends that are similar to those reported in the literature. Potential practical applications of the formulation and the solution approach are discussed.

Analytical boundary of the workspace for general 3-DOF mechanisms

An analytical method is presented to obtain all surfaces en veloping the workspace of a general 3-DOF mechanism. The method is applicable to kinematic chains that can be mod eled using the Denavit-Hartenberg representation for serial kinematic chains or its modification for closed-loop kinematic chains. The method developed is based upon analytical crite ria for determining singular behavior of the mechanism. By manipulating the Jacobian of the underlying mechanism, first- order singularities are computed. These singularities are then substituted into the constraint equation to parameterize singu lar surfaces representing barriers to motion. Singular surfaces are those resultihg from a singular behavior of a joint gen eralized coordinate, allowing the manipulator to lose one or more degrees of mobility. These surfaces are then intersected to determine singular curves, which represent the manipulator losing at least two degrees of mobility. Difficulties in sepa rating singular behaviors at points along singular curves are encountered. Also, difficulties in computing tangents at the intersections of singular curves are addressed. These difficul ties are resolved using an analysis of a quadratic form of the intersection of singular surfaces. An example is presented to validate the theory. Although the methods used are numerical, the main result of this work is the ability to analytically define boundary surfaces of the workspace.

On the determination of starting points for parametric surface intersections

Two numerical algorithms for computing starting points on the curve of intersection between two parametric surfaces are presented. The problem of determining intersection curves between two surfaces is analytically formulated by parametrizing inequality constraints into equality constraints and augmenting the constraint function. The first method uses an iterative optimization formulation and an iterative conjugate gradient algorithm to minimize a function comprising the vector of coordinates and a weighted constraint term. The second method uses the Moore-Penrose pseudo inverse of the constraint function to determine a starting point. Numerical examples are presented to validate both methods. Both methods require an initial point on one of the surfaces. Numerical examples illustrating the validity of the presented methods are discussed. The local versus the global views of the intersection problem in terms of iterative and recursive subdivision methods are addressed. Difficulties in determining more than one point are also illustrated using examples. The two algorithms are compared by studying their computational complexity. The Moore-Penrose inverse method has showed superior efficiency in the computational complexity, number of iterations needed, and time for conversion to a starting point. It is also shown that the Moore-Penrose inverse converges to a starting point in cases where the iterative optimization method does not.

Optimization-based trajectory planning of the human upper body

This paper presents studies of the coordination of human upper body voluntary movement. A minimum-jerk 3D model is used to obtain the desired path in Cartesian space, which is widely used in the prediction of human reach movement. Instead of inverse kinematics, a direct optimization approach is used to predict each joints profile (a spline curve). This optimization problem has four cost function terms: (1) Joint displacement function that evaluates displacement of each joint away from its neutral position; (2) Inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial target point to the final target point; (3) The non-smoothness function of the trajectory, which is the second derivative of the joint trajectory; (4) The non-continuity function, which consists of the amplitudes of joint angle rates at the initial and final target points, in order to emphasize smooth starting and ending conditions. This direct optimization technique can be used for potentially any number of degrees of freedom (DOF) system and it reduces the cost associated with certain inverse kinematics approaches for resolving joint profiles. This paper presents a high redundant upper-body modeling with 15 DOFs. Illustrative examples are presented and an interface is set up to visualize the results.