Smooth and Time-Optimal Trajectory Generation for High Speed Machine Tools

In machining complex dies, molds, aerospace and automotive parts, or biomedical components, it is crucial to minimize the cycle time, which reduces costs, while preserving the quality and tolerance integrity of the part being produced. To meet the demands for high quality finishes and low production costs in machining parts with complex geometry, computer numerical control (CNC) machine tools must be equipped with spline interpolation, feedrate modulation, and feedrate optimization capabilities. This thesis presents the development of novel trajectory generation algorithms for Non Uniform Rational B-Spline (NURBS) toolpaths that can be implemented on new low-cost CNC's, as well as, in conjunction with existing CNC's. In order to minimize feedrate fluctuations during the interpolation of NURBS toolpaths, the concept of the feed correction polynomial is applied. Feedrate fluctuations are reduced from around 40 % for natural interpolation to 0.1 % for interpolation with feed correction. Excessive acceleration and jerk in the axes are also avoided. To generate jerk-limited feed motion profiles for long segmented toolpaths, a generalized framework for feedrate modulation, based on the S-curve function, is presented. Kinematic compatibility conditions are derived to ensure that the position, velocity, and acceleration profiles are continuous and that the jerk is limited in all axes. This framework serves as the foundation for the proposed heuristic feedrate optimization strategy in this thesis. Using analytically derived kinematic compatibility equations and an efficient bisection search algorithm, the command feedrate for each segment is maximized. Feasible solutions must satisfy the optimization constraints on the velocity, control signal (i.e. actuation torque), and jerk in each axis throughout the trajectory. The maximized feedrates are used to generate near-optimal feed profiles that have shorter cycle times, approximately 13-26% faster than the feed profiles obtained using the worst-case curvature approach, which is widely used in industrial CNC interpolators. The effectiveness of the NURBS interpolation, feedrate modulation and feedrate optimization techniques has been verified in 3-axis machining experiments of a biomedical implant

A Novel Approach for NURBS Interpolation with Minimal Feed Rate Fluctuation Based on Improved Adams-Moulton Method

In order to reduce the feed rate fluctuation of interpolation, a novel approach for NURBS interpolation with minimal feed rate fluctuation based on improved Adams-Moulton (IAM) method is proposed. At first, the representation and calculation of NURBS curve interpolation are described. Then, the constraints of feeding step length are firstly given out to calculate the minimal hoping feeding step length and the detailed IAM method of NURBS curve interpolation is presented. Finally, simulations and experiments are carried out to verify the feasibility and applicability of proposed IAM method

Arc-Length Parameterized NURBS Tool Path Generation and Velocity Profile Planning for Accurate 3-Axis Curve Milling

In modern industrial CNC (Computer Numerical Control) machining processes, the pursuing of higher accuracy and efficiency has always been one of the most important tasks to be discussed and studied. A lot of proposed algorithms are developed in order to optimize the machining performance in either of the above focused domains. Nevertheless, there is forever a trade-off between gaining less machining error and providing higher feed rate. As for machining a free-shaped curve (e.g., Bezier curves, B-splines and NURBS) in a three-dimensional space, a better manner to balance out the aforementioned trade-offs turns out to be even more critical and essential. The conventional iterative function used for tool path generation could cause feed rate fluctuation during the actual machining, and it thus might lead to failure on constraining the error within the machining accuracy requirement. Another potential problem occurs when the machining process comes across into a relatively high curvature segment with the prescribed high feed rate, due to the machine axial acceleration limit, the machine may not be able to maintain the tool tip trajectory within the error tolerance. Therefore, a new approach to NURBS tool path generation for high feed rate machining is proposed. In this work, several criterions are set for checking the viability of the prescribed feed rate and adjusting it according to the actual shape of the objective curve and the capability of the machine. After the offline feed rate viability check and readjustment, a new iterative algorithm based on the arc-length re-parameterized NURBS function would be implemented to calculate the tool path in real-time. By using this proposed method, the feed rate fluctuation is diminished and the overall efficiency of the machining process would have been optimized under the condition of accuracy guaranteed

Piecewise Arc-Length Parameterized NURBS Tool Paths Generation for 3-Axis CNC Machining of Accurate, Smooth Sculptured Surfaces

In current industrial applications many engineering parts having complex shapes are designed using sculptured surfaces in CAD system. Due to the lack of smooth motions and accurate machining of these surfaces using standard linear and circular motions in conventional CNC machines, new commercial CNC systems are equipped with parametric curve interpolation function. However, in some applications these surfaces can be very complex that are susceptible to gouging and due to the approximation of; CL-path in CAM system and path parameter in real –time, high machining accuracy, smooth kinematic and feed-rate profiles, are difficult to achieve. This dissertation focuses on developing algorithms that generate tool paths in NURBS form for smooth, high speed and accurate sculptured surface machining. The first part of the research identifies and eliminates gouge cutter location (CL) point from the tool path. The proposed algorithm uses global optimization technique (Particle Swarm Optimization) to check all the CC-points along a tool-path with high accuracy, and only gouging free CC-points are used to generate the set of valid CL-points. Mathematical models have been developed and implemented to cover most of the cutter shapes, used in the industry. In the second phase of the research, all valid CL-points along the tool-path are used to generate CL-path in B-spline form. The main contribution of this part is to formulate an error function of the offset approximation and to represent it in NURBS form to globally bound the approximation errors. Based on this error function, an algorithm is proposed to generate tool-paths in B-spline from with; globally controlled accuracy, fewer control points and low function degree, compared to its contemporaries. The proposed approach thus presents an error-bounded method for B-spline curve approximation to the ideal CL-path within the accuracy. This part of research has two components, one is for 2½- axis (pocket) and the other one is for 3-axis (surface) CNC machining. The third part deals with the problem of CL-path parameter estimation during machining in real time. Once the gouging free CL-path in NURBS form with globally controlled accuracy is produced, it is re-parameterized with approximate arc-length in the off-line stage. The main features of this work are; (1) sampling points and calculating their approximate arc-lengths within error bound by decomposing the input path into Bezier curve segments, (2) fitting the NURBS curve with approximate arc-length parameter to the sample points until the path and parameterization errors are within the tolerance, and (3) segment the curve into pieces with different feed rates if during machining the cutter trajectory errors are beyond the tolerance at highly curved regions in the NURBS tool path

Path Planning For Persistent Surveillance Applications Using Fixed-Wing Unmanned Aerial Vehicles

This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles (UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission, fixed wing vehicles have maneuver constraints that can limit their performance in this role. Current technology vehicles are capable of long duration flight with a minimal acoustic footprint while carrying an array of cameras and sensors. Both military tactical and civilian safety applications can benefit from this technology. We make three main contributions: C1 A sequential path planner that generates a C2 flight plan to persistently acquire a covering set of data over a user designated area of interest. The planner features the following innovations: • A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length • A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction • A smooth path generator that provides C2 routes that satisfy user specified curvature constraints C2 A set of algorithms to coordinate multiple UAVs, including mission commencement from arbitrary locations to the start of a coordinated mission and de-confliction of paths to avoid collisions with other vehicles and fixed obstacles iv C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing validated through flight test experiments on multiple platforms. A variety of tests and platforms are discussed. The algorithms presented are based on a technical approach with approximately equal emphasis on analysis, computation, dynamic simulation, and flight test experimentation. Our planner (C1) directly takes into account vehicle maneuverability and agility constraints that could otherwise render simple solutions infeasible. This is especially important when surveillance objectives elevate the importance of optimized paths. Researchers have devel oped a diverse range of solutions for persistent surveillance applications but few directly address dynamic maneuver constraints. The key feature of C1 is a two stage sequential solution that discretizes the problem so that graph search techniques can be combined with parametric polynomial curve generation. A method to abstract the kino-dynamics of the aerial platforms is then presented so that a graph search solution can be adapted for this application. An A* Traveling Salesman Problem (TSP) algorithm is developed to search the discretized space using the abstract distance metric to acquire more data or avoid obstacles. Results of the graph search are then transcribed into smooth paths based on vehicle maneuver constraints. A complete solution for a single vehicle periodic tour of the area is developed using the results of the graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm (C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and to ensure there are no collisions at any of the path intersections. We present a toolbox of spline-based algorithms (C3) to streamline the development of C2 continuous paths with numerical stability. These tools are applied to an aerial persistent surveillance application to illustrate their utility. Comparisons with other parametric poly nomial approaches are highlighted to underscore the benefits of the B-spline framework. Performance limits with respect to feasibility constraints are documented

A survey of free software for the design, analysis, modelling, and simulation of an unmanned aerial vehicle

The objective of this paper is to analyze free software for the design, analysis, modelling, and simulation of an unmanned aerial vehicle (UAV). Free software is the best choice when the reduction of production costs is necessary; nevertheless, the quality of free software may vary. This paper probably does not include all of the free software, but tries to describe or mention at least the most interesting programs. The first part of this paper summarizes the essential knowledge about UAVs, including the fundamentals of flight mechanics and aerodynamics, and the structure of a UAV system. The second section generally explains the modelling and simulation of a UAV. In the main section, more than 50 free programs for the design, analysis, modelling, and simulation of a UAV are described. Although the selection of the free software has been focused on small subsonic UAVs, the software can also be used for other categories of aircraft in some cases; e.g. for MAVs and large gliders. The applications with an historical importance are also included. Finally, the results of the analysis are evaluated and discussed—a block diagram of the free software is presented, possible connections between the programs are outlined, and future improvements of the free software are suggested. © 2015, CIMNE, Barcelona, Spain.Internal Grant Agency of Tomas Bata University in Zlin [IGA/FAI/2015/001, IGA/FAI/2014/006

A Biomimetic, Energy-Harvesting, Obstacle-Avoiding, Path-Planning Algorithm for UAVs

This dissertation presents two new approaches to energy harvesting for Unmanned Aerial Vehicles (UAV). One method is based on the Potential Flow Method (PFM); the other method seeds a wind-field map based on updraft peak analysis and then applies a variant of the Bellman-Ford algorithm to find the minimum-cost path. Both methods are enhanced by taking into account the performance characteristics of the aircraft using advanced performance theory. The combined approach yields five possible trajectories from which the one with the minimum energy cost is selected. The dissertation concludes by using the developed theory and modeling tools to simulate the flight paths of two small Unmanned Aerial Vehicles (sUAV) in the 500 kg and 250 kg class. The results show that, in mountainous regions, substantial energy can be recovered, depending on topography and wind characteristics. For the examples presented, as much as 50% of the energy was recovered for a complex, multi-heading, multi-altitude, 170 km mission in an average wind speed of 9 m/s. The algorithms constitute a Generic Intelligent Control Algorithm (GICA) for autonomous unmanned aerial vehicles that enables an extraction of atmospheric energy while completing a mission trajectory. At the same time, the algorithm automatically adjusts the flight path in order to avoid obstacles, in a fashion not unlike what one would expect from living organisms, such as birds and insects. This multi-disciplinary approach renders the approach biomimetic, i.e. it constitutes a synthetic system that “mimics the formation and function of biological mechanisms and processes.

CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics 1999

These proceedings represent a collection of the latest advances in aeroelasticity and structural dynamics from the world community. Research in the areas of unsteady aerodynamics and aeroelasticity, structural modeling and optimization, active control and adaptive structures, landing dynamics, certification and qualification, and validation testing are highlighted in the collection of papers. The wide range of results will lead to advances in the prediction and control of the structural response of aircraft and spacecraft

Formulation of a Path-Following Joint for Multibody System Dynamics

The development and validation of a new multibody joint that constrains a body to follow a spatial path and an orientation defined by a user is presented. The resulting joint has a single degree of freedom (DOF), and maintains equivalent kinematic behaviour when compared to higher-fidelity models. As such, it is referred to as a single-DOF equivalent kinematic (SEK) joint. The primary application of this joint is in the reduction of complex multibody systems, specifically vehicle suspensions. The first formulation of the joint is developed using the user interface of MapleSim. Starting with a planar particle joint, the theory is extended to a full 3D rigid body constraint. At each development stage, the joint is successfully validated against conventional models in both Adams and MapleSim. This formulation of the joint results in the kinematic pair being represented by a system of differential algebraic equations (DAEs) which is not the desired functionality, and so a second formulation is developed. By removing the constraint of using the MapleSim user interface, the formulation can be developed from first principles. Using the path-length as the coordinate for the joint, and the Frenet-Serret equations to compute the motion and reaction spaces, the kinematic pair can be represented by a single ordinary differential equation (ODE). The theory is implemented in the MapleSim source code using the symbolic computing language Maple. The theory of the SEK joint can be extended to create different joints. The first is the compliant SEK joint. In this version of the joint, the body is constrained to move along a spatial path using a simple linear bushing model. The compliant SEK joint is useful for modeling the suspension systems of passenger cars as bushings are used extensively in these systems to increase passenger comfort. The second extension is to add an additional DOF to the SEK joint to created the double-DOF equivalent kinematic (DEK) joint. The DEK joint is useful for modelling steered suspension systems as the steering introduces an additional DOF to the suspension. The envelope of motion for the steered wheel is a surface rather than a spatial line. Once the joints are successfully validated, three example applications of the joint are shown. In the first, rigid, compliant and steered suspension models are developed and compared against high-fidelity models in Adams/Car and MapleSim. Next, a full vehicle model is assembled using the suspension models and compared against an equivalent high-fidelity full vehicle model built in MapleSim. The comparisons show the accuracy of the SEK joint as well as the simulation speed improvements it can offer compared with conventional modelling techniques. The second example, from the domain of biomechanics, shows a knee model created using the SEK joint. Finally, a roller coaster model is created to demonstrate the flexibility of the path generation algorithm to create splines that represent complex paths