A mathematical model for a Two-Span Web Roller machine is defined in order to facilitate motion planning, motion tracking and state observer design for tracking web tension and web velocity. Differential Flatness is utilized to create reference trajectories that are tracked with a high convergence rate. Flatness also allows for nominal input torque generation without integration. Constraints on the inputs are satisfied through the motion planning phase. A partial state feedback linearization is performed and an exponential tracking dynamic feedback controller is defined. An exponential Kalman-related tension observer is also defined with semi-optimal gain formulation. The observer takes advantage of the bilinearity of the dynamics up to additive output nonlinearity. The closed-loop system is simulated in MatLab with comparisons to reference trajectories previously employed in literature. The importance of proper motion planning is demonstrated by producing excellent performance compared with existing tracking and tension observing methods.

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Computer-aided fixture planning (CAFP) is an essential part of Computer-aided design and manufacturing (CAD/CAM) integration. Proper fixture planning can dramatically reduce the manufacturing cost, the lead-time, and labor skill requirements in product manufacturing. However, fixture planning is a highly experience-based activity. Due to the extreme diversity and complexity of manufacturing workpieces and processes, there are not many fixture planning tools available for industry applications. Moreover, existing CAFP methods rarely consider integrating fixture environmental factors into fixture planning. Automatic fixture planning using VR can provide a viable way for industries. This thesis develops automated approaches to fixture planning in a virtual environment (VE). It intends to address two important issues: automatic algorithms for fixture planning, and the VE to support high fidelity evaluation of fixture planning. The system consists of three parts including fixture assembly planning, feasibility analysis of assembly tools, and motion planning for fixture loading and unloading. The virtual fixture planning system provides the fixture designer a tool for fixture planning and evaluation. Geometrical algorithms are developed to facilitate the automatic reasoning. A Web-based VE for fixture planning is implemented. The three-dimensional (3D) model visualization enables the fixture simulation and validation effectively to investigate existing problems. Approaches to construct desktop-based large VEs are also investigated. Cell segmentation methods and dynamic loading strategies are investigated to improve the rendering performance. Case studies of virtual building navigation and product assembly simulations are conducted. The developed algorithms can successfully generate the assembly plan, validate the assembly tools, and generate moving paths for fixture design and applications. The VE is intuitive and sufficient to support fixture planning, as well as other virtual design and manufacturing tasks.

10th IFAC Symposium on Robot Control International Federation of Automatic Control September 5-7, 2012. Dubrovnik, Croatia

Robotic motion planning aspires to match the ease and efficiency with which humans move through and interact with their environment. Yet state of the art robotic planners fall short of human abilities; they are slower in computation, and the results are often of lower quality. One stumbling block in traditional motion planning is that points and paths are often considered in isolation. Many planners fail to recognize that substantial shared information exists among path alternatives. Exploitation of the geometric and topological relationships among path alternatives can therefore lead to increased efficiency and competency. These benefits include: better-informed path sampling, dramatically faster collision checking, and a deeper understanding of the trade-offs in path selection. In path sampling, the principle of locality is introduced as a basis for constructing an adaptive, probabilistic, geometric model to influence the selection of paths for collision test. Recognizing that collision testing consumes a sizable majority of planning time and that only collision-free paths provide value in selecting a path to execute on the robot, this model provides a significant increase in efficiency by circumventing collision testing paths that can be predicted to collide with obstacles. In the area of collision testing, an equivalence relation termed local path equivalence, is employed to discover when the work of testing a path has been previously performed. The swept volumes of adjoining path alternatives frequently overlap, implying that a continuum of intermediate paths exists as well. By recognizing such neighboring paths with related shapes and outcomes, up to 90% of paths may be tested implicitly in experiments, bypassing the traditional, expensive collision test and delivering a net 300% boost in collision test performance. Local path equivalence may also be applied to the path selection problem in order to recognize higher-level navigation options and make smarter choices. This thesis presents theoretical and experimental results in each of these three areas, as well as inspiration on the connections to how humans reason about moving through spaces.

This thesis addresses the problem of motion planning for autonomous robots, given a map and an estimate of the robot pose within it. The motion planning problem for a mobile robot can be defined as computing a trajectory in an environment from one pose to another while avoiding obstacles and optimizing some objective such as path length or travel time, subject to constraints like vehicle dynamics limitations. More complex planning problems such as multi-robot planning or complete coverage of an area can also be defined within a similar optimization structure. The computational complexity of path planning presents a considerable challenge for real-time execution with limited resources and various methods of simplifying the problem formulation by discretizing the solution space are grouped under the class of discrete planning methods. The approach suggests representing the environment as a roadmap graph and formulating shortest path problems to compute optimal robot trajectories on it. This thesis presents two main contributions under the framework of discrete planning. The first contribution addresses complete coverage of an unknown environment by a single omnidirectional ground rover. The 2D occupancy grid map of the environment is first converted into a polygonal representation and decomposed into a set of convex sectors. Second, a coverage path is computed through the sectors using a hierarchical inter-sector and intra-sector optimization structure. It should be noted that both convex decomposition and optimal sector ordering are known NP-hard problems, which are solved using a greedy cut approximation algorithm and Travelling Salesman Problem (TSP) heuristics, respectively. The second contribution presents multi-robot path-planning strategies for recharging autonomous robots performing a persistent task. The work considers the case of surveillance missions performed by a team of Unmanned Aerial Vehicles (UAVs). The goal is to plan minimum cost paths for a separate team of dedicated charging robots such that they rendezvous with and recharge all the UAVs as needed. To this end, planar UAV trajectories are discretized into sets of charging locations and a partitioned directed acyclic graph subject to timing constraints is defined over them. Solutions consist of paths through the graph for each of the charging robots. The rendezvous planning problem for a single recharge cycle is formulated as a Mixed Integer Linear Program (MILP), and an algorithmic approach, using a transformation to the TSP, is presented as a scalable heuristic alternative to the MILP. The solution is then extended to longer planning horizons using both a receding horizon and an optimal fixed horizon strategy. Simulation results are presented for both contributions, which demonstrate solution quality and performance of the presented algorithms.

Computer-aided fixture planning (CAFP) is an essential part of Computer-aided design and manufacturing (CAD/CAM) integration. Proper fixture planning can dramatically reduce the manufacturing cost, the lead-time, and labor skill requirements in product manufacturing. However, fixture planning is a highly experience-based activity. Due to the extreme diversity and complexity of manufacturing workpieces and processes, there are not many fixture planning tools available for industry applications. Moreover, existing CAFP methods rarely consider integrating fixture environmental factors into fixture planning. Automatic fixture planning using VR can provide a viable way for industries. This thesis develops automated approaches to fixture planning in a virtual environment (VE). It intends to address two important issues: automatic algorithms for fixture planning, and the VE to support high fidelity evaluation of fixture planning. The system consists of three parts including fixture assembly planning, feasibility analysis of assembly tools, and motion planning for fixture loading and unloading. The virtual fixture planning system provides the fixture designer a tool for fixture planning and evaluation. Geometrical algorithms are developed to facilitate the automatic reasoning. A Web-based VE for fixture planning is implemented. The three-dimensional (3D) model visualization enables the fixture simulation and validation effectively to investigate existing problems. Approaches to construct desktop-based large VEs are also investigated. Cell segmentation methods and dynamic loading strategies are investigated to improve the rendering performance. Case studies of virtual building navigation and product assembly simulations are conducted. The developed algorithms can successfully generate the assembly plan, validate the assembly tools, and generate moving paths for fixture design and applications. The VE is intuitive and sufficient to support fixture planning, as well as other virtual design and manufacturing tasks.

Whether it is a car, a mobile phone, or a computer, we are noticing how automation and production with robots plays an important role in the industry of our modern world. We find it in factories, manufacturing products, automotive cruise control, construction equipment, autopilot on airplanes, and countless other industrial applications.         Automation technology can vary greatly depending on the field of application. On one end, we have systems that are operated by the user and rely fully on human ability. Examples of these are heavy-mobile equipment, remote controlled systems, helicopters, and many more. On the other end, we have autonomous systems that are able to make algorithmic decisions independently of the user.         Society has always envisioned robots with the full capabilities of humans. However, we should envision applications that will help us increase productivity and improve our quality of life through human-robot collaboration. The questions we should be asking are: “What tasks should be automated?'', and “How can we combine the best of both humans and automation?”. This thinking leads to the idea of developing systems with some level of autonomy, where the intelligence is shared between the user and the system. Reasonably, the computerized intelligence and decision making would be designed according to mathematical algorithms and control rules.         This thesis considers these topics and shows the importance of fundamental mathematics and control design to develop automated systems that can execute desired tasks. All of this work is based on some of the most modern concepts in the subjects of robotics and control, which are synthesized by a method known as the Virtual Holonomic Constraints Approach. This method has been useful to tackle some of the most complex problems of nonlinear control, and has enabled the possibility to approach challenging academic and industrial problems. This thesis shows concepts of system modeling, control design, motion analysis, motion planning, and many other interesting subjects, which can be treated effectively through analytical methods. The use of mathematical approaches allows performing computer simulations that also lead to direct practical implementations.

Creating realistic human animations is a difficult and time consuming job. One of the best solutions known is motion capture, which is an expensive process. Manipulating existing motion data instead of capturing new data is an efficient way of creating new human animations. In this thesis, we review the current techniques for animation, navigation and ways of manipulating motion data. We discuss strengths and weaknesses of interpolation techniques for creating new motions. Then we present a system that uses existing motion data to create a motion graph and automatically creates new motion data for character navigation suitable for user requirements. Finally, we give experimental results and discuss possible uses of the system.

In the field of robotics there is a great interest in developing strategies and algorithms to reproduce human-like behavior. One can think of human-like machines that may replace humans in hazardous working areas, perform enduring assembly tasks, serve the elderly and handicapped, etc. The main challenges in the development of such robots are, first, to construct sophisticated electro-mechanical humanoids and, second, to plan and control human-like motor patterns. A promising idea for motion planning and control is to reparameterize any somewhat coordinated motion in terms of virtual holonomic constraints, i.e. trajectories of all degrees of freedom of the mechanical system are described by geometric relations among the generalized coordinates. Imposing such virtual holonomic constraints on the system dynamics allows to generate synchronized motor patterns by feedback control. In fact, there exist consistent geometric relations in ordinary human movements that can be used advantageously. In this thesis the virtual constraints approach is extended to a wider and rigorous use for analyzing, planning and reproducing human-like motions based on mathematical tools previously utilized for very particular control problems. It is often the case that some desired motions cannot be achieved by the robot due to limitations in available actuation power. This constraint rises the question of how to modify the mechanical design in order to achieve better performance. An underactuated planar two-link robot is used to demonstrate that springs can complement the actuation in parallel to an ordinary motor. Motion planning is carried out for the original robot dynamics while the springs are treated as part of the control action with a torque profile suited to the preplanned trajectory. Another issue discussed in this thesis is to find stable and unstable (hybrid) limit cycles for passive dynamic walking robots without integrating the full set of differential equations. Such procedure is demonstrated for the compass-gait biped by means of optimization with a reduced number of initial conditions and parameters to search. The properties of virtual constraints and reduced dynamics are exploited to solve this problem.