Efficient motion planning for problems lacking optimal substructure

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra's algorithm. Our algorithm runs in $O\left((n_B\cdot n) \log( n_B\cdot n) + n_B\cdot m\right)$ time, where~$n$ and $m$ are the number of vertices and edges of the graph, respectively, and $n_B$ is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm

www.springerreference.com/docs/html/chapterdbid/60497.html Mechanical Computing: The Computational Complexity of Physical Devices

- Mechanism: A machine or part of a machine that performs a particular task computation: the use of a computer for calculation.- Computable: Capable of being worked out by calculation, especially using a computer.- Simulation: Used to denote both the modeling of a physical system by a computer as well as the modeling of the operation of a computer by a mechanical system; the difference will be clear from the context. Definition of the Subject Mechanical devices for computation appear to be largely displaced by the widespread use of microprocessor-based computers that are pervading almost all aspects of our lives. Nevertheless, mechanical devices for computation are of interest for at least three reasons: (a) Historical: The use of mechanical devices for computation is of central importance in the historical study of technologies, with a history dating back thousands of years and with surprising applications even in relatively recent times. (b) Technical & Practical: The use of mechanical devices for computation persists and has not yet been completely displaced by widespread use of microprocessor-based computers. Mechanical computers have found applications in various emerging technologies at the micro-scale that combine mechanical functions with computational and control functions not feasible by purely electronic processing. Mechanical computers also have been demonstrated at the molecular scale, and may also provide unique capabilities at that scale. The physical designs for these modern micro and molecular-scale mechanical computers may be based on the prior designs of the large-scale mechanical computers constructed in the past. (c) Impact of Physical Assumptions on Complexity of Motion Planning, Design, and Simulation: The study of computation done by mechanical devices is also of central importance in providing lower bounds on the computational resources such as time and/or space required to simulate a mechanical syste

Problems

I. Definition of the Subject and Its Importanc

Creating movable interfaces by micro-powder injection moulding

This paper presents a novel in situ technique to produce articulated components with high-precision, micro-scale movable interfaces by micro-powder injection moulding (μPIM). The presented process route is based on the use of micro-scale sacrificial layer between the movable subcomponents which is eliminated during the debinding step, creating a dimensionally-controlled, micro-scale mobile interface. The fabrication technique combines the advantages of micro-powder overmoulding, catalytic debinding and sintering. The demonstrated example was a finger bone prosthesis joint consisting of two sub-components with an interface between components of 200 μm in size. The geometries of the sub-components were designed such that they are inseparable throughout the process whilst allowing them to move relative to each other after the debinding stage. The components produced showed the feasibility of the process route to produce readily-assembled meso-, and potentially micro-, scale articulated system

Machine Systems for Exploration and Manipulation: A Conceptual Framework and Method of Evaluation

A conceptual approach to describing and evaluating problem-solving by robotic systems is offered. One particular problem of importance to the field of robotics, disassembly, is considered. A general description is provided of an effector system equipped with sensors that interacts with objects for purposes of disassembly and that learns as a result. The system\u27s approach is bottom up, in that it has no a priori knowledge about object categories. It does, however, have pre-existing methods and strategies for exploration and manipulation. The sensors assumed to be present are vision, proximity, tactile, position, force, and thermal. The system\u27s capabilities are described with respect to two phases: object exploration and manipulation. Exploration takes the form of executing exploratory procedures, algorithms for determining the substance, structure, and mechanical properties of objects. Manipulation involves manipulatory operators, defined by the type of motion, nature of the end-effector configuration, and precise parameterization. The relation of the hypothesized system to existing implementations is described, and a means of evaluating it is also proposed

Fixtureless automated incremental sheet metal forming

Die-based forming is a technology used by many industries to form metal panels. However, this method of forming lacks flexibility and cost effectiveness. In such cases, manual panel beating is typically undertaken for incremental forming of metal panels. Manual panel forming is a highly skilled operation with very little documentation and is disappearing due to non-observance and a lack of interest. Confederation of British Metal forming (CBM) and Institution of Sheet Metal Engineering (ISME) have realised the need for capturing and understanding manual skills used by panel beaters to preserve the knowledge. At the same time, industries seek for alternative panel forming solutions to produce high quality and cost-effective parts at low volume and reduce the repetitive, yet adaptive parts of the panel forming process to free up skilled workers to concentrate on the forming activities that are more difficult to automate. Incremental forming technologies, currently in practice, lack adaptability as they require substantial fixtures and dedicated tools. In this research a new proof-of-concept fixtureless automated sheet metal forming approach was developed on the basis of human skills captured from panel beaters. The proposed novel approach, named Mechatroforming®, consists of integrated mechanisms to form simple sheet metal parts by manipulating the workpiece using a robotic arm under a repetitive hammering tool. Predictive motion planning based on FEA was analysed and the manual forming skills were captured using a motion capture system. This facilitated the coordinated hammering and motion of the part to produce the intended shape accurately. A 3D measurement system with a vertical resolution of 50μm was also deployed to monitor the formation of the parts and make corrections to the forming path if needed. Therefore, the developed mechatronic system is highly adjustable by robotic motion and was closed loop via the 3D measurement system. The developed automated system has been tested rigorously, initially for bowl shape parts to prove the principle. The developed system which is 98% repeatable for depth and diameter, is able to produce targeted bowl shape parts with ±1% dimensional accuracy, high surface quality, and uniform material thickness of 0.95mm when tested with aluminium. It is envisaged that by further research, the proposed approach can be extended to form irregular and more complicated shapes that are highly in demand in various industries