Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed by Ordinary Differential Equations

The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. Treatment of small geometric uncertainty in the context of manufacturing tolerances is a well studied topic. Traditional sequential design methodologies have recently been replaced by concurrent optimal design methodologies where optimal system parameters are simultaneously determined along with optimally allocated tolerances; this allows to reduce manufacturing costs while increasing performance. However, the state of the art approaches remain limited in that they can only treat geometric related uncertainties restricted to be small in magnitude. This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems governed by ordinary differential equations. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Additionally, uncertainties are allowed to be large in magnitude and the governing constitutive relations may be highly nonlinear. In the proposed framework, uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments of the uncertain system to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that is off-set from the traditional deterministic optimal trade-off curve. The Pareto off-set is shown to be a result of the additional statistical moment information formulated in the objective and constraint relations that account for the system uncertainties. Therefore, the Pareto trade-off curve from the new framework characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost. A kinematic tolerance analysis case-study is presented first to illustrate how the proposed methodology can be applied to treat geometric tolerances. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost, accounting for the entire family of systems within the associated probability space. This case-study highlights the general nature of the new framework which is capable of optimally allocating uncertainties of multiple types and with large magnitudes in a single calculation

Combining Dynamic Modeling With Geometric Constraint Management to Support Low Clearance Virtual Manual Assembly

This research presents a novel approach to virtual assembly that combines dynamic modeling with geometric constraint-based modeling to support low clearance manual assembly of CAD models. This is made possible by utilizing the boundary representation solid model data available in most contemporary CAD representations, which enables (a) accurate collision/physics calculations on exact model definitions, and (b) access to geometric features. Application of geometric constraints during run-time, aid the designer during assembly of the virtual models. The feasibility of the approach is demonstrated using a pin and hole assembly example. Results that demonstrate the method give the user the ability to assemble parts without requiring extensive CAD preprocessing and without over constraining the user to arrive at predetermined final part orientations. Assembly is successful with diametral clearance as low as 0.0001 mm, as measured between a 26 mm diameter hole and pin

Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

Sketching as a solid modeling tool

Journal ArticleThis paper describes 'Quick-sketch', a 2-d and 3d modeling tool for pen based computers. Users of this system define a model by simple pen strokes drawn directly on the screen of a pen-based PC. Lines, circles, arcs, or B-spline curves are automatically distinguished and interpreted from these strokes. The system also automatically determines relations, such as right angles, tangencies, symmetry, and parallelism, from the sketch input. These relationships are then used to clean up the drawing by making the approximate relationships exact. Constraints are established to maintain the relationships during further editing. A constraint maintenance system, which is based on gestural manipulation and soft constraints, is employed in this system. Several techniques for sketch based definitions of 3d objects are provided as well, including extrusion, surface of revolution, ruled surfaces and sweep. Features can be sketched on the surface of a 3d object, using the same 2d and 3d techniques. This way, objects of medium complexity can be sketched in seconds. The system can be viewed as a front-end to more sophisticated modeling, rendering or animation environments, serving as a hand sketching tool in the preliminary design phase

Combining physical constraints with geometric constraint-based modeling for virtual assembly

The research presented in this dissertation aims to create a virtual assembly environment capable of simulating the constant and subtle interactions (hand-part, part-part) that occur during manual assembly, and providing appropriate feedback to the user in real-time. A virtual assembly system called SHARP System for Haptic Assembly and Realistic Prototyping is created, which utilizes simulated physical constraints for part placement during assembly.;The first approach taken in this research attempt utilized Voxmap Point Shell (VPS) software for implementing collision detection and physics-based modeling in SHARP. A volumetric approach, where complex CAD models were represented by numerous small cubic-voxel elements was used to obtain fast physics update rates (500--1000 Hz). A novel dual-handed haptic interface was developed and integrated into the system allowing the user to simultaneously manipulate parts with both hands. However, coarse model approximations used for collision detection and physics-based modeling only allowed assembly when minimum clearance was limited to ∼8-10%.;To provide a solution to the low clearance assembly problem, the second effort focused on importing accurate parametric CAD data (B-Rep) models into SHARP. These accurate B-Rep representations are used for collision detection as well as for simulating physical contacts more accurately. A new hybrid approach is presented, which combines the simulated physical constraints with geometric constraints which can be defined at runtime. Different case studies are used to identify the suitable combination of methods (collision detection, physical constraints, geometric constraints) capable of best simulating intricate interactions and environment behavior during manual assembly. An innovative automatic constraint recognition algorithm is created and integrated into SHARP. The feature-based approach utilized for the algorithm design, facilitates faster identification of potential geometric constraints that need to be defined. This approach results in optimized system performance while providing a more natural user experience for assembly

A Sparse Multi-Scale Algorithm for Dense Optimal Transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of an algorithm to solve large dense problems by considering a sequence of sparse problems instead. The algorithm lends itself to being combined with a hierarchical multi-scale scheme. Any existing discrete solver can be used as internal black-box.Several cost functions, including the noisy squared Euclidean distance, are explicitly detailed. We observe a significant reduction of run-time and memory requirements.Comment: Published "online first" in Journal of Mathematical Imaging and Vision, see DO

Combining Geometric Constraints With Physics Modeling for Virtual Assembly Using SHARP

This research combines physics-based and constraint-based approaches for virtual assembly simulations where geometric constraints are created or deleted within the virtual environment at runtime. In addition, this research provides a solution to low clearance assembly by utilizing B-Rep data representation of complex CAD models for accurate collision/physics results. These techniques are demonstrated in the SHARP software (System for Haptic Assembly and Realistic Prototyping). Combining physics-based and constraint-based techniques and operating on accurate B-rep data, SHARP can now assemble parts with 0.001% clearance and can accurately detect collision responses with 0.0001mm accuracy. Case studies are presented which can be used to identify the suitable combination of methods capable of best simulating intricate interactions and environment behavior during manual assembly

Virtual reality for assembly methods prototyping: a review

Assembly planning and evaluation is an important component of the product design process in which details about how parts of a new product will be put together are formalized. A well designed assembly process should take into account various factors such as optimum assembly time and sequence, tooling and fixture requirements, ergonomics, operator safety, and accessibility, among others. Existing computer-based tools to support virtual assembly either concentrate solely on representation of the geometry of parts and fixtures and evaluation of clearances and tolerances or use simulated human mannequins to approximate human interaction in the assembly process. Virtual reality technology has the potential to support integration of natural human motions into the computer aided assembly planning environment (Ritchie et al. in Proc I MECH E Part B J Eng 213(5):461–474, 1999). This would allow evaluations of an assembler’s ability to manipulate and assemble parts and result in reduced time and cost for product design. This paper provides a review of the research in virtual assembly and categorizes the different approaches. Finally, critical requirements and directions for future research are presented

A constraint-based methodology for product design with virtual reality

This paper presents a constraint-based methodology for product design with advanced virtual reality technologies. A hierarchically structured and constraint-based data model is developed to support product design from features to parts and further to assemblies in a VR environment. Product design in the VR environment is performed in an intuitive manner through precise constraint-based manipulations. Constraint-based manipulations are accompanied with automatic constraint recognition and precise constraint satisfaction to establish constraints between objects, and are further realized by allowable motions for precise 3D interactions in the VR environment. The allowable motions are represented as a mathematical matrix and derived from constraints between objects by constraint solving. A procedure-based degrees-of-freedom combination approach is presented for 3D constraint solving. A rule-based constraint recognition engine is developed for both constraint-based manipulations and implicitly incorporating constraints into the VR environment. An intuitive method is presented for recognizing pairs of mating features between assembly components. Examples are presented to demonstrate the efficacy of the proposed methodology