Fast algorithms for collision and proximity problems involving moving geometric objects

Consider a set of geometric objects, such as points, line segments, or axes-parallel hyperrectangles in \IR^d, that move with constant but possibly different velocities along linear trajectories. Efficient algorithms are presented for several problems defined on such objects, such as determining whether any two objects ever collide and computing the minimum inter-point separation or minimum diameter that ever occurs. The strategy used involves reducing the given problem on moving objects to a different problem on a set of static objects, and then solving the latter problem using techniques based on sweeping, orthogonal range searching, simplex composition, and parametric search

Articular human joint modelling

Copyright @ Cambridge University Press 2009.The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints

Sweep-Line Extensions to the Multiple Object Intersection Problem: Methods and Applications in Graph Mining

Identifying and quantifying the size of multiple overlapping axis-aligned geometric objects is an essential computational geometry problem. The ability to solve this problem can effectively inform a number of spatial data mining methods and can provide support in decision making for a variety of critical applications. The state-of-the-art approach for addressing such problems resorts to an algorithmic paradigm, collectively known as the sweep-line or plane sweep algorithm. However, its application inherits a number of limitations including lack of versatility and lack of support for ad hoc intersection queries. With these limitations in mind, we design and implement a novel, exact, fast and scalable yet versatile, sweep-line based algorithm, named SLIG. The key idea of our algorithm lies in constructing an auxiliary data structure when the sweep line algorithm is applied, an intersection graph. This graph can effectively be used to provide connectivity properties among overlapping objects and to inform answers to ad hoc intersection queries. It can also be employed to find the location and size of the common area of multiple overlapping objects. SLIG performs significantly faster than classic sweep-line based algorithms, it is more versatile, and provides a suite of powerful querying capabilities. To demonstrate the versatility of our SLIG algorithm we show how it can be utilized for evaluating the importance of nodes in a trajectory network - a type of dynamic network where the nodes are moving objects (cars, pedestrians, etc.) and the edges represent interactions (contacts) between objects as defined by a proximity threshold. The key observation to address the problem is that the time intervals of these interactions can be represented as 1-dimensional axis-aligned geometric objects. Then, a variant of our SLIG algorithm, named SLOT, is utilized that effectively computes the metrics of interest, including node degree, triangle membership and connected components for each node, over time

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

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

Hierarchical Manipulation for Constructing Free Standing Structures

abstract: In order for a robot to solve complex tasks in real world, it needs to compute discrete, high-level strategies that can be translated into continuous movement trajectories. These problems become increasingly difficult with increasing numbers of objects and domain constraints, as well as with the increasing degrees of freedom of robotic manipulator arms. The first part of this thesis develops and investigates new methods for addressing these problems through hierarchical task and motion planning for manipulation with a focus on autonomous construction of free-standing structures using precision-cut planks. These planks can be arranged in various orientations to design complex structures; reliably and autonomously building such structures from scratch is computationally intractable due to the long planning horizon and the infinite branching factor of possible grasps and placements that the robot could make. An abstract representation is developed for this class of problems and show how pose generators can be used to autonomously compute feasible robot motion plans for constructing a given structure. The approach was evaluated through simulation and on a real ABB YuMi robot. Results show that hierarchical algorithms for planning can effectively overcome the computational barriers to solving such problems. The second part of this thesis proposes a deep learning-based algorithm to identify critical regions for motion planning. Further investigation is done whether these learned critical regions can be translated to learn high-level landmark actions for automated planning.Dissertation/ThesisMasters Thesis Computer Science 201

GPU-based proximity query processing on unstructured triangular mesh model

This paper presents a novel proximity query (PQ) approach capable to detect the collision and calculate the minimal Euclidean distance between two non-convex objects in 3D, namely the robot and the environment. Such approaches are often considered as computationally demanding problems, but are of importance to many applications such as online simulation of haptic feedback and robot collision-free trajectory. Our approach enables to preserve the representation of unstructured environment in the form of triangular meshes. The proposed PQ algorithm is computationally parallel so that it can be effectively implemented on graphics processing units (GPUs). A GPU-based computation scheme is also developed and customized, which shows >200 times faster than an optimized CPU with single core. Comprehensive validation is also conducted on two simulated scenarios in order to demonstrate the practical values of its potential application in image-guided surgical robotics and humanoid robotic control.published_or_final_versio