Multi-Criteria Optimization Manipulator Trajectory Planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Design, Analysis, and Fabrication of a Snake-Inspired Robot with a Rectilinear Gait

Snake-inspired robots display promise in areas such as search, rescue and reconnaissance due to their ability to locomote through tight spaces. However, several specific issues regarding the design and analysis must be addressed in order to better design them. This thesis develops kinematic and dynamic models for a class of snake-inspired gait known as a rectilinear gait, where mechanism topology changes over the course of the gait. A model using an Eulerian framework and Coulomb friction yields torque expressions for the joints of the robot. B-spline curves are then used to generate a parametric optimization formulation for joint trajectory generation. Exact gradient computation of the torque functions is presented. A parametric model is used to describe the performance effects of changing system parameters such as mass, length, and motor speed. Finally, a snake-inspired robot is designed and fabricated in order to demonstrate both the vertical rectilinear gait and a modular, molded design aimed at reducing the cost of fabrication

Design, Analysis, and Fabrication of a Snake-Inspired Robot with a Rectilinear Gait

Snake-inspired robots display promise in areas such as search, rescue and reconnaissance due to their ability to locomote through tight spaces. However, several specific issues regarding the design and analysis must be addressed in order to better design them. This thesis develops kinematic and dynamic models for a class of snake-inspired gait known as a rectilinear gait, where mechanism topology changes over the course of the gait. A model using an Eulerian framework and Coulomb friction yields torque expressions for the joints of the robot. B-spline curves are then used to generate a parametric optimization formulation for joint trajectory generation. Exact gradient computation of the torque functions is presented. A parametric model is used to describe the performance effects of changing system parameters such as mass, length, and motor speed. Finally, a snake-inspired robot is designed and fabricated in order to demonstrate both the vertical rectilinear gait and a modular, molded design aimed at reducing the cost of fabrication

Modelling, synthesis and model-based motion planning for hyper-redundant, binary actuated manipulators

Die Untersuchung von schwer zu erreichenden Hohlräumen durch schmale Zugänge wird im technischen Umfeld als Boroskopie und in der Medizin als Endoskopie bezeichnet. Wenn neben der reinen Inspektion auch eine Manipulation erfolgen soll, wird ergänzend zu einer guten Anpassbarkeit an gekrümmte Pfade auch eine stabile Arbeitsplattform zur Aufnahme von Manipulationskräften benötigt. Einen Ansatz, die daraus resultierenden Anforderungen an die verwendeten Systeme zu adressieren, stellen schlangenartige Roboter dar. Ihre hyperredundante Struktur aus einzelnen Stellgliedern bietet eine vielseitige Positionierbarkeit. Die Verwendung von binären, kippstabilen Aktoren beschränkt zwar den Arbeitsraum auf wenige diskrete Punkte, bietet aber – in Abhängigkeit vom Antriebsmechanismus – besonders hohe Haltemomente und ermöglicht damit eine gezielte Systemversteifung. Eine Kombination beider Ansätze zur Klasse der binär aktuierten, hyperredundanten Manipulatoren ist in der Lage, diese Anforderungen zu erfüllen, jedoch existiert deutlicher Forschungsbedarf hinsichtlich Methoden zur optimalen Auslegung sowie zur gezielten Verfolgung von Referenzpfaden, sodass Kern der vorliegenden Arbeit die Erforschung der modellbasierten Bewegungsplanung dieser Roboterklasse ist. Voraussetzung für eine hohe Pfadfolgegenauigkeit ist, dass der Manipulator sich grundsätzlich gut an einen vorgegebenen Referenzpfad anschmiegen kann. Der Einschränkungsgrad durch die diskrete Positionierbarkeit des Manipulators ist dabei abhängig von den geometrischen Parametern der einzelnen Segmente. Die Untersuchungen in dieser Arbeit zeigen, dass durch die Analyse kinematischer Leistungsmerkmale, wie Arbeitsraum(-dichte) oder erzielbarer Krümmungsradius, kein allgemeingültiges optimales Design gefunden werden kann. Daher wird eine Maßsynthese unter Berücksichtigung von Randbedingungen entworfen, in der optimale geometrische Parameter eines einzelnen binären Aktors synthetisiert werden. Darauf aufbauend wird eine Pfadverfolgung gemäß dem „Follow-the-Leader“-Prinzip erarbeitet. Grundidee ist, dass das Endeffektorsegment den Referenzpfad exploriert, während alle weiteren Aktoren dem führenden Segment automatisch folgen. Da binäre Aktoren einen nicht-kontinuierlichen Schaltprozess aufweisen, wird ein modellbasierter Ansatz für die Bestimmung optimaler Schaltsequenzen vorgeschlagen, die zu jedem Zeitpunkt eine hohe Pfadtreue garantieren. Die anschließende experimentelle Evaluation erfolgt nach der Modellierung und Identifikation relevanter Parameter für den Prototyp einer elektromagnetischen Kippaktorkette. Grundsätzlich kann die Funktionsfähigkeit der in dieser Arbeit erforschten Methoden zur Bewegungsplanung sowohl in der Simulation als auch experimentell nachgewiesen werden.The investigation of difficult to reach cavities through narrow accesses is called borescopy in the technical environment and endoscopy in medicine. If manipulation is to be performed in addition to pure inspection, a stable working platform is required to withstand manipulation forces in combination with good adaptability to curved paths. One approach to address the resulting requirements for the systems used are snake-like robots. Their hyper-redundant structure of individual actuators allows for versatile positioning. Although the use of binary, tilt-stable actuators limits the working space to a few discrete points, they offer - depending on the drive mechanism - particularly high holding torques and thus enable a targeted system stiffening. A combination of both approaches to the class of binary actuated, hyper-redundant manipulators is able to meet the required requirements, however, there is a clear need for research into methods for optimal design and the targeted pursuit of reference paths, so that the core of the present work consists the investigation of model-based motion planning of this robot class. A prerequisite for a high path following accuracy is that the manipulator is able to adapt well to a given reference path. The degree of limitation due to discrete positionability of the manipulator depends on the geometric parameters of the individual segments. The studies in this thesis show that the analysis of kinematic performance characteristics, such as work space (density) or achievable radius of curvature, does not lead to a generally valid optimal design. Therefore, a dimensional synthesis is developed under consideration of boundary conditions, in which optimal geometric parameters of a single binary actuator are synthesized. Based on this, a path following according to the "Follow-the-Leader"principle is elaborated. The basic idea is that the end effector segment explores the reference path, while all other actuators automatically follow the leading segment. Since binary actuators have a discontinuous switching process, a model-based approach is proposed for determining optimal switching sequences that guarantee high path accuracy at all times. The subsequent experimental evaluation is performed after modelling and identification of relevant parameters for the prototype of an electromagnetic tilting actuator chain. In principle, the functionality of the motion planning methods investigated in this thesis are proven both in simulation and experimentally