Rapid Mapping and Exploration of Configuration Space

Nelaturi, Saigopal; Lysenko, Mikola; Shapiro, Vadim

doi:10.1115/1.4005776

Cited by 7 publications

(7 citation statements)

References 32 publications

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“…Other applications show the computation of workspaces of parallel linkages, like the 4-bar chain [23]. Recently Nelaturi et al showed that group morphology can be used to determine the accessible positions and orientations of a weld gun [24].…”

Section: Group Morphology and Spectral Methodsmentioning

confidence: 99%

Configuration Workspaces of Series-Parallel Mechanisms

McCarthy

Lysenko

Shapiro

2012

Volume 4: 36th Mechanisms and Robotics Conference, Parts a and B

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The workspace of a mechanism is the set of positions and orientations that is reachable by its end effector. Workspaces have numerous applications, including motion planning, mechanism design, and manufacturing process planning, but their representation and computation is challenging due to high dimensionality and geometric/topological complexity. We propose a new formulation of the workspace computation problem for a large class of mechanisms represented by series-parallel constraint graphs. A wide variety of allowable constraints include all lower pair, some higher pair, and non-collision constraints. We show that the workspace of such mechanisms may be computed by a constraint propagation algorithm. After the space of all rigid body motions is discretized, these operations can be efficiently implemented using the Fast Fourier Transform and a depth first search. In contrast to algebraic formulations, the proposed method assures that all configurations in the computed workspace not only satisfy pairwise constraints but can be reached without breaking and reassembling the mechanism.

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Section: Group Morphology and Spectral Methodsmentioning

confidence: 99%

Configuration Workspaces of Series-Parallel Mechanisms

McCarthy

Lysenko

Shapiro

2012

Volume 4: 36th Mechanisms and Robotics Conference, Parts a and B

Self Cite

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“…For 5-axis machining applications, one of the six DOF for rotation around the tool axis is deemed redundant and the problem is simplified by assuming simple shapes for the rotating tool's closure such as a flat/ball-end cylinders, approximating reachability by visibility, and so on [34][35][36][37][38][39][40][41]. However, the computations can be dramatically simplified by sampling-based approximations [42]. It has been shown that collision measures can be obtained as convolutions of indicator functions of the two bodies [43], and computed rapidly via fast Fourier transform (FFT) if these functions are sampled over uniform grids (i.e., voxelization) [44].…”

Section: Related Workmentioning

confidence: 99%

Topology optimization with accessibility constraint for multi-axis machining

Mirzendehdel

Behandish

Nelaturi

2020

Computer-Aided Design

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In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part's performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

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“…Rather, they are often expressed as set constraints, i.e., statements in the language of sets (e.g., in terms of affine transformations, Boolean operations, and containment) rather than the language of realvalued functions used for (in)equality constraints in TO. A broad class of inverse problems in practical design and manufacturing reduce to solving set constraints formulated in the configuration space of rigid motions [6,[65][66][67].…”

Section: Design For Motion-related Constraintsmentioning

confidence: 99%

“…For instance, if we impose a constraint on the maximal stress as in (6), we cannot define a realistic TSF due to stress concentration. The simplest model of stress concentration yields an infinite maximal stress σ Ω (x) ∼ O( −0.5 ) near an infinitesimal radius of curvature → 0 + , hence T i (x; Ω) ∼ O( −3.5 ) → +∞ when defined for the maximal stress as in (6). In practice, one can alleviate this issue by using a volumetric integral (e.g., the p−norm) of 12 This is the actual motivation behind using a volumetric measure of the inclusion in the denominator of (75) to normalize volumetric measures in the numerator.…”

Section: Limitations Of Sensitivity-based Explorationmentioning

confidence: 99%

Exploring feasible design spaces for heterogeneous constraints

Mirzendehdel

Behandish

Nelaturi

2019

Computer-Aided Design

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We demonstrate an approach of exploring design spaces to simultaneously satisfy kinematics-and physics-based requirements. We present a classification of constraints and solvers to enable postponing optimization as far down the design workflow as possible. The solvers are organized into two broad classes of design space 'pruning' and 'exploration' by considering the types of constraints they can satisfy. We show that pointwise constraints define feasible design subspaces that can be represented and computed as first-class entities by their maximal feasible elements. The design space is pruned upfront by intersecting maximal elements, without premature optimization. To solve for other constraints, we apply topology optimization (TO), starting from the pruned feasible space. The optimization is steered by a topological sensitivity field (TSF) that measures the global changes in violation of constraints with respect to local topological punctures. The TSF for global objective functions is augmented with TSF for global constraints, and penalized/filtered to incorporate local constraints, including set constraints converted to differentiable (in)equality constraints. We demonstrate application of the proposed workflow to nontrivial examples in design and manufacturing. Among other examples, we show how to explore pruned design spaces via TO to simultaneously satisfy physics-based constraints (e.g., minimize compliance and mass) as well as kinematics-based constraints (e.g., maximize accessibility for machining).

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Rapid Mapping and Exploration of Configuration Space

Cited by 7 publications

References 32 publications

Configuration Workspaces of Series-Parallel Mechanisms

Configuration Workspaces of Series-Parallel Mechanisms

Topology optimization with accessibility constraint for multi-axis machining

Exploring feasible design spaces for heterogeneous constraints

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