A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima

Manipulability in trajectory tracking for constrained redundant manipulators via sequential quadratic programming

Trajectory tracking methods for constrained redundant manipulators are presented in this thesis, where the end-effector of a redundant serial manipulator has to track a desired trajectory while some points on its kinematic chain satisfy one or more constraints. In addition, two manipulability indexes are taken into account in order to optimize the trajectory. The first index is defined in terms of the geometric Jacobian of the manipulator in the constrained configuration. The second index is based on the constrained Jacobian, which maps velocities from joint space to task space, taking into account the holonomic constraints. Three methods for solving the trajectory tracking problem are discussed. The first two, kinematic control (KC) and quadratic programming (QP), are widely discussed in literature. The third, sequential quadratic programming (SQP), is a new approach, unlike KC or QP, has as advantages (despite some shortcomings) not explicitly depend on pseudoinverse Jacobian, derivative from the desired trajectory and linearization of indexes or constraints. A discussion of these three methods is presented in terms of tracking error, constraint violation, singularity distance, among others through experiments performed on a Baxter collaborative robot.Métodos de rastreamento de trajetória para manipuladores redundantes restritos são apresentados nesta tese, onde o efetuador de um manipulador serial redundante tem que rastrear uma trajetória desejada enquanto alguns pontos em sua cadeia cinemática satisfazem uma ou mais restrições. Além disso, dois índices de manipulabilidade são levados em consideração a fim de otimizar a trajetória para evitar singularidades. O primeiro índice é definido em função do jacobiano geométrico do manipulador na configuração restrita. O segundo índice é baseado no Jacobiano restrito, o qual mapeia velocidades no espaço das juntas para a espaço da tarefa, levando em conta as restrições holonômicas. Três métodos para resolver o problema de rastreamento de trajetória são discutidos. Os dois primeiros, controle cinemático e programação quadrática (QP), são amplamente discutidos na literatura. O terceiro, programação quadrática sequencial (SQP), é uma nova abordagem, diferentemente do controle cinemático ou QP, tem como vantagens (apesar de algumas deficiências) não depender explicitamente da pseudo-inversa de jacobianos, derivadas da trajetória desejada e linearização de índices ou restrições. Uma discussão desses três métodos é apresentada em termos de erro de rastreamento, violação da restrição, distância de singularidades, entre outros através de experimentos realizados em um robô colaborativo Baxter

Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots

In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip\u27s following error

Optimization Approach for Inverse Kinematic Solution

Inverse kinematics of serial or parallel manipulators can be computed from given Cartesian position and orientation of end effector and reverse of this would yield forward kinematics. Which is nothing but finding out end effector coordinates and angles from given joint angles. Forward kinematics of serial manipulators gives exact solution while inverse kinematics yields number of solutions. The complexity of inverse kinematic solution arises with the increment of degrees of freedom. Therefore it would be desired to adopt optimization techniques. Although the optimization techniques gives number of solution for inverse kinematics problem but it converses the best solution for the minimum function value. The selection of suitable optimization method will provides the global optimization solution, therefore, in this paper proposes quaternion derivation for 5R manipulator inverse kinematic solution which is later compared with teachers learner based optimization (TLBO) and genetic algorithm (GA) for the optimum convergence rate of inverse kinematic solution. An investigation has been made on the accuracies of adopted techniques and total computational time for inverse kinematic evaluations. It is found that TLBO is performing better as compared GA on the basis of fitness function and quaternion algebra gives better computational cost

Coordinated Motion Control of Multiple Robotic Devices for Welding and Redundancy Coordination through Constrained Optimization in Cartesian Space

In this paper we consider the problem of coordinating multiple motion devices for welding. We focus on the problem of coordinating a positioning table and a seven axis manipulator, given the parametric definition of a trajectory on a weld piece. The problem is complex as there are more than nine axis involved and a number of permutations are possible which achieve the same motions of the weld torch. The system is redundant and the robot has singular configurations. As a result, manual programming of the robot system is rather complex. Our approach to the coordination problem is based on subdivision of constraints. The welding table is coordinated to ensure down-handed welding convention, while the seven axis robot (a six axis Cybotech WV15 robot and track) are coordinated to track the weld point. The coordination is achieved by keeping the robot in good maneuverability position, so as to avoid the robots singularity conditions and motion limits of the track. We were able to express the singularity conditions in terms of cartesian coordinates [I]. As a result, we could obtain analytic solution to our optimization of the maneuversability and therefore avoid using known pseudoinverse techniques which are known to exhibit inaccuracies [2]. The output of our optimization process is the positions of the track and the robot end-effector, these positions are used to generate the joint angles of the arm by inverse kinematics

Continuous-time recurrent neural networks for quadratic programming: theory and engineering applications.

Liu Shubao.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 90-98).Abstracts in English and Chinese.Abstract --- p.i摘要 --- p.iiiAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Time-Varying Quadratic Optimization --- p.1Chapter 1.2 --- Recurrent Neural Networks --- p.3Chapter 1.2.1 --- From Feedforward to Recurrent Networks --- p.3Chapter 1.2.2 --- Computational Power and Complexity --- p.6Chapter 1.2.3 --- Implementation Issues --- p.7Chapter 1.3 --- Thesis Organization --- p.9Chapter I --- Theory and Models --- p.11Chapter 2 --- Linearly Constrained QP --- p.13Chapter 2.1 --- Model Description --- p.14Chapter 2.2 --- Convergence Analysis --- p.17Chapter 3 --- Quadratically Constrained QP --- p.26Chapter 3.1 --- Problem Formulation --- p.26Chapter 3.2 --- Model Description --- p.27Chapter 3.2.1 --- Model 1 (Dual Model) --- p.28Chapter 3.2.2 --- Model 2 (Improved Dual Model) --- p.28Chapter II --- Engineering Applications --- p.29Chapter 4 --- KWTA Network Circuit Design --- p.31Chapter 4.1 --- Introduction --- p.31Chapter 4.2 --- Equivalent Reformulation --- p.32Chapter 4.3 --- KWTA Network Model --- p.36Chapter 4.4 --- Simulation Results --- p.40Chapter 4.5 --- Conclusions --- p.40Chapter 5 --- Dynamic Control of Manipulators --- p.43Chapter 5.1 --- Introduction --- p.43Chapter 5.2 --- Problem Formulation --- p.44Chapter 5.3 --- Simplified Dual Neural Network --- p.47Chapter 5.4 --- Simulation Results --- p.51Chapter 5.5 --- Concluding Remarks --- p.55Chapter 6 --- Robot Arm Obstacle Avoidance --- p.56Chapter 6.1 --- Introduction --- p.56Chapter 6.2 --- Obstacle Avoidance Scheme --- p.58Chapter 6.2.1 --- Equality Constrained Formulation --- p.58Chapter 6.2.2 --- Inequality Constrained Formulation --- p.60Chapter 6.3 --- Simplified Dual Neural Network Model --- p.64Chapter 6.3.1 --- Existing Approaches --- p.64Chapter 6.3.2 --- Model Derivation --- p.65Chapter 6.3.3 --- Convergence Analysis --- p.67Chapter 6.3.4 --- Model Comparision --- p.69Chapter 6.4 --- Simulation Results --- p.70Chapter 6.5 --- Concluding Remarks --- p.71Chapter 7 --- Multiuser Detection --- p.77Chapter 7.1 --- Introduction --- p.77Chapter 7.2 --- Problem Formulation --- p.78Chapter 7.3 --- Neural Network Architecture --- p.82Chapter 7.4 --- Simulation Results --- p.84Chapter 8 --- Conclusions and Future Works --- p.88Chapter 8.1 --- Concluding Remarks --- p.88Chapter 8.2 --- Future Prospects --- p.88Bibliography --- p.8