Abstract: Techniques for level-set based shape optimization with shape constraints include simulating a state of a current shape of a component, calculating a sensitivity of an objective function to with respect to modification to the current shape based on the simulated shape based on the simulated state, generating a source function for an optimization equation based on the sensitivity, adding one or more constraint terms to the optimization equation based on one or more constraints on an interface of the shape to generate a constrained optimization equation, solving the constrained optimization equation to generate a solution to the constrained optimization equation, updating a velocity field based on the solution to the constrained optimization equation, solving a transport function based on the updated velocity field to generate a solution of the transport equation, and updating the current shape based on the solution to the transport equation to generate an updated shape.

Abstract: In various embodiments, a generative design application can leverage multi-disciplinary optimization to solve a design problem associated with a 3D model and interdependent design variables. The generative design application includes an optimization engine that can solve the design problem, or portions thereof, by iteratively performing optimization techniques on the interdependent design variables to generate an 3D model that maximizes or minimizes one or more objectives and meets one or more constraints, while simultaneously considering the effect of each interdependency of the design variables. Furthermore, the generative design application can leverage a natural language interface to augment the creation of the design problem for optimization. The generative design application can also leverage free-form deformation during generative design to parameterize a portion of the 3D model as part of the design problem.

Abstract: In various embodiments, a generative design application can leverage multi-disciplinary optimization to solve a design problem associated with a 3D model and interdependent design variables. The generative design application includes an optimization engine that can solve the design problem, or portions thereof, by iteratively performing optimization techniques on the interdependent design variables to generate an 3D model that maximizes or minimizes one or more objectives and meets one or more constraints, while simultaneously considering the effect of each interdependency of the design variables. Furthermore, the generative design application can leverage a natural language interface to augment the creation of the design problem for optimization. The generative design application can also leverage free-form deformation during generative design to parameterize a portion of the 3D model as part of the design problem.

Abstract: In various embodiments, a generative design application can leverage multi-disciplinary optimization to solve a design problem associated with a 3D model and interdependent design variables. The generative design application includes an optimization engine that can solve the design problem, or portions thereof, by iteratively performing optimization techniques on the interdependent design variables to generate an 3D model that maximizes or minimizes one or more objectives and meets one or more constraints, while simultaneously considering the effect of each interdependency of the design variables. Furthermore, the generative design application can leverage a natural language interface to augment the creation of the design problem for optimization. The generative design application can also leverage free-form deformation during generative design to parameterize a portion of the 3D model as part of the design problem.

Abstract: A computer-implemented method for controlling a robot, the method comprising: determining a first value for a first joint parameter associated with a first continuum joint included in the robot and a first value for a second joint parameter associated with the first continuum joint, wherein the first joint parameter indicates a bending radius of a flexible portion of the continuum joint, and the second joint parameter indicates a rotation of the flexible portion of the continuum joint with respect to a base portion of the first continuum joint; and positioning an end portion of the robot at a final target location based on the first value of the first joint parameter and the first value of the second joint parameter.

Abstract: Techniques for generative design include a computer-implemented method for solving a design problem comprising initializing values for one or more categorical and continuous design variables, and performing a design iteration by generating sample vectors for each of one or more categorical design variables based on the categorical design variable probabilities, solving one or more governing equations for the design problem based on values of the continuous design variables and the sample vectors, computing a value of one or more constraint functions and an objective function, computing first gradients of the objective function and the constraint functions with respect to each of the continuous design variables, computing second gradients of the objective function and the constraint functions with respect to the categorical design variable probabilities, and updating values for the continuous design variables based on the first gradients and values for the categorical design variable probabilities based on the

Abstract: Techniques for interactive generative design with sensitivity analysis and probability visualization for categorical design variables include a computer-implemented method for evaluating an impact of categorical design variables on a design problem solution comprises receiving information regarding choices for one or more categorical design variables associated with each of a plurality of design members of a design problem, determining a respective sensitivity of an objective function to the choices for the one or more categorical design variables for each design member of the plurality of design members, determining a respective visual aspect for each design member based on the respective sensitivity, displaying, on a user interface, a graphical depiction of the plurality of design members, wherein each design member is displayed using the respective visual aspect, and displaying, on the user interface, a key for interpreting the respective visual aspects.

Abstract: Techniques for generative design include a computer-implemented method for solving a design problem comprising initializing values for one or more categorical design variable probabilities and one or more continuous design variables, and performing a design iteration by performing one or more iterations to update the categorial design variable probabilities by generating sample vectors for each of one or more categorical design variables based on the categorical design variable probabilities, computing first gradients of an objective function and one or more constraint functions with respect to the categorical design variable probabilities, and updating values for the categorical design variable probabilities based on the first gradients, then updating the sample vectors based on the updated categorical design variable probability values, computing second gradients of the objective and constraint functions with respect to each of the continuous design variables, and updating values for the continuous design v

Abstract: A design engine automates portions of a mechanical assembly design process. The design engine generates a user interface that exposes tools for capturing input data related to the design problem. Based on the input data, the design engine performs various operations to generate a formalized problem definition that can be processed by a goal-driven optimization algorithm. The goal-driven optimization algorithm generates a spectrum of potential design options. Each design option describes a mechanical assembly representing a potential solution to the design problem.

Abstract: A design engine systematically explores a design space associated with a design problem related to mechanical assemblies. The design engine implements a constraint programming approach to produce mechanical assembly configurations that adhere to a set of design constraints. For each feasible configuration, the design engine then optimizes various parameters to generate design options that meet a set of design objectives. With these techniques, the design space can be explored very quickly to generate significantly more feasible design options for the mechanical assembly than possible with conventional manual approaches. Accordingly, numerous design options can be generated that may otherwise never be produced using those conventional approaches.

Abstract: A design engine systematically explores a design space associated with a design problem related to mechanical assemblies. The design engine implements a constraint programming approach to produce mechanical assembly configurations that adhere to a set of design constraints. For each feasible configuration, the design engine then optimizes various parameters to generate design options that meet a set of design objectives. With these techniques, the design space can be explored very quickly to generate significantly more feasible design options for the mechanical assembly than possible with conventional manual approaches. Accordingly, numerous design options can be generated that may otherwise never be produced using those conventional approaches.

Abstract: A design engine implements a probabilistic approach to generating designs that exposes automatically-generated design knowledge to the user during operation. The design engine interactively generates successive populations of designs based on a problem definition associated with a design problem and/or a previously-generated population of designs. During the above design process, the design engine generates a design knowledge graphical user interface (GUI) that graphically exposes various types of design knowledge to the user. In particular, the design engine generates a design variable dependency GUI that visualizes various dependencies between designs variables. The design engine also generates a design evolution GUI that animates the evolution of designs across the successive design populations. Additionally, the design engine generates a design exploration GUI that facilitates the user exploring various statistical properties of automatically-generated designs.

Abstract: A design engine generates a configuration option that includes a specific arrangement of interconnected mechanical elements adhering to one or more design constraints. Each element within a given configuration option is defined by a set of design variables. The design engine implements a parametric optimizer to optimize the set of design variables associated with each configuration option. For a given configuration option, the parametric optimizer discretizes continuous equations governing the physical dynamics of the configuration. The parametric optimizer then determines the gradient of an objective function based on the discretized equations the gradient of objective and constraint functions based on discrete direct differentiation method or discrete adjoint variable method derived directly from the discretized motion equations. Then, the parametric optimizer traverses a design space where the configuration option resides to reduce improve the objective function, thereby optimizing the design variables.

Abstract: A design engine implements a probabilistic approach to generating designs that exposes automatically-generated design knowledge to the user during operation. The design engine interactively generates successive populations of designs based on a problem definition associated with a design problem and/or a previously-generated population of designs. During the above design process, the design engine generates a design knowledge graphical user interface (GUI) that graphically exposes various types of design knowledge to the user. In particular, the design engine generates a design variable dependency GUI that visualizes various dependencies between designs variables. The design engine also generates a design evolution GUI that animates the evolution of designs across the successive design populations. Additionally, the design engine generates a design exploration GUI that facilitates the user exploring various statistical properties of automatically-generated designs.

Abstract: A design engine implements a probabilistic approach to generating designs that exposes automatically-generated design knowledge to the user during operation. The design engine interactively generates successive populations of designs based on a problem definition associated with a design problem and/or a previously-generated population of designs. During the above design process, the design engine generates a design knowledge graphical user interface (GUI) that graphically exposes various types of design knowledge to the user. In particular, the design engine generates a design variable dependency GUI that visualizes various dependencies between designs variables. The design engine also generates a design evolution GUI that animates the evolution of designs across the successive design populations. Additionally, the design engine generates a design exploration GUI that facilitates the user exploring various statistical properties of automatically-generated designs.

Abstract: A design engine implements a probabilistic approach to generating designs for computer-aided design (CAD) assemblies. The design engine initially generates a population of designs based on a problem definition associated with a design problem. Each design includes a randomly-generated set of design values assigned to various design variables. The design engine repairs any infeasible designs in the population of designs and then executes a dynamic simulation with the population of designs. The design engine selects the most performant designs and identifies, based on those performant designs, design variables that are dependent on one another. The design engine generates a probability model indicating conditional probabilities between design values associated with dependent design variables. The design engine then iteratively samples the probability model to generate a subsequent population of designs.

Abstract: A computer-implemented method for generating a design for a continuum robot includes: generating a first plurality of candidate designs for the continuum robot, wherein each candidate design included in the first plurality of candidate designs is based on a first set of values for a set of design parameters; determining a first performance value for each candidate design included in the first plurality of candidate designs; based at least in part on the first performance values, selecting a subset of candidate designs from the first plurality of candidate designs; and based on the subset of candidate designs, generating a second plurality of candidate designs for the continuum robot, wherein each candidate design included in the second plurality of candidate designs is based on a second set of values for the set of design parameters.

Abstract: A computer-implemented method for controlling a robot, the method comprising: determining a first value for a first joint parameter associated with a first continuum joint included in the robot and a first value for a second joint parameter associated with the first continuum joint, wherein the first joint parameter indicates a bending radius of a flexible portion of the continuum joint, and the second joint parameter indicates a rotation of the flexible portion of the continuum joint with respect to a base portion of the first continuum joint; and positioning an end portion of the robot at a final target location based on the first value of the first joint parameter and the first value of the second joint parameter.

Abstract: Techniques are disclosed for designing structures using a torsion-deformable spatial beam element. The beam element can be represented using the absolute nodal coordinate formulation, or any other technically feasible formulation. At each of one or more time steps, the Bishop frame is used to generate local coordinate systems along a center line of the beam element, which are used to compute a potential energy of the beam element. Thereafter, a derivative of the potential energy is plugged into equations of motion that are solved to determine an updated state of the beam element. A representation of the updated beam element can also be rendered and displayed via a graphical user interface.

Abstract: A design engine implements a probabilistic approach to generating designs that exposes automatically-generated design knowledge to the user during operation. The design engine interactively generates successive populations of designs based on a problem definition associated with a design problem and/or a previously-generated population of designs. During the above design process, the design engine generates a design knowledge graphical user interface (GUI) that graphically exposes various types of design knowledge to the user. In particular, the design engine generates a design variable dependency GUI that visualizes various dependencies between designs variables. The design engine also generates a design evolution GUI that animates the evolution of designs across the successive design populations. Additionally, the design engine generates a design exploration GUI that facilitates the user exploring various statistical properties of automatically-generated designs.