A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.     

A general formulation and approach to constrained,continuum manipulation

A continuum manipulator is particularly suitable for performing tasks in cluttered environments with limited space for maneuvering and is even more flexible with a mobile base. However, to perform a task, the motion of a continuum manipulator must not only avoid obstacles, i.e. subject to environment constraints, but also satisfy certain position and orientation constraints imposed by the task. An important open issue is how to enable a (mobile) continuum manipulator to perform a task-constrained motion while avoiding obstacles. In this paper, we introduce a general formulation of the problem and an approach to automatic planning of mobile continuum manipulation under general task and environmental constraints. The effectiveness of the approach is verified by simulation and real experiments.     

Collision-free control of an omni-directional vehicle

This study addresses the problem of controlling an omni-directional vehicle with both state and control dependent constraints. The task of the vehicle is to attain its desired final position given in the task space. The control constraints resulting from the physical abilities of actuators driving the vehicle wheels are also taken into account during the robot movement. The problem of collision avoidance is solved here based on an exterior penalty function approach which results in smooth vehicle velocities near obstacles. Provided that, a solution to the aforementioned vehicle task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results carried out for the omni-directional vehicle operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.     

Sliding Mode Adaptive Neural-Network Control for Nonholonomic Mobile Modular Manipulators

A general mobile modular manipulator can be defined as a m-wheeled holonomic/nonholonomic mobile platform combining with a n-degree of freedom modular manipulator. This paper presents a sliding mode adaptive neural-network controller for trajectory following of nonholonomic mobile modular manipulators in task space. Dynamic model for the entire mobile modular manipulator is established in consideration of nonholonomic constraints and the interactive motions between the mobile platform and the onboard modular manipulator. Multilayered perceptrons (MLP) are used as estimators to approximate the dynamic model of the mobile modular manipulator. Sliding mode control and direct adaptive technique are combined together to suppress bounded disturbances and modeling errors caused by parameter uncertainties. Simulations are performed to demonstrate that the dynamic modeling method is valid and the controller design algorithm is effective.     

Path following by the end-effector of a redundant manipulator operating in a dynamic environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.     

Motion Control of a Nonholonomic Mobile Manipulator in Task Space

In this paper, the motion control of a mobile manipulator subjected to nonholonomic constraints is investigated. The control objective is to design a computed‐torque controller based on the coupled dynamics of the mobile manipulator. The proposed controller achieves the capability of simultaneous tracking of a reference velocity for the mobile base and a reference trajectory for the end‐effector. The aforementioned reference velocity and trajectory are defined in the task space, such task setting imitates the actual working conditions of a mobile manipulator and thus makes the control problem practical. To solve this tracking problem, a steering velocity is firstly designed based on the first‐order kinematic model of the nonholonomic mobile base via dynamic feedback linearization. The main merit of the proposed steering velocity design is that it directly utilizes the reference velocity set in the task space without requiring the knowledge of a reference orientation. A torque controller is subsequently developed based on a proposed Lyapunov function which explicitly considers the coupled dynamics of the mobile manipulator to ensure the mobile base and end‐effector track the reference velocity and trajectory respectively. This proposed computed‐torque controller is able to realize asymptotic stability of both the base velocity tracking error and the end‐effector motion tracking error. Simulations are conducted to demonstrate the effectiveness of the proposed controller.     

On trajectory and force tracking control of constrained mobile manipulators with parameter uncertainty

This paper studies the trajectory and force tracking control problem of mobile manipulators subject to holonomic and nonholonomic constraints with unknown inertia parameters. Adaptive controllers are proposed based on a suitable reduced dynamic model, the defined reference signals and the mixed tracking errors. The proposed controllers not only ensure the entire state of the system to asymptotically converge to the desired trajectory but also ensure the constraint force to asymptotically converge to the desired force. A detailed numerical example is presented to illustrate the developed methods.     

Path-constrained control of a redundant manipulator in a task space

This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.     

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.     

Analysis and Control for an Omnidirectional Mobile Manipulator

This paper describes analysis and control for a holonomic omnidirectional mobile manipulator, in which the holonomic omnidirectional platform consists of three lateral orthogonal wheel assemblies and a mounted manipulator with three rotational joints is located at the center of gravity of the platform. We first introduce the kinematic model for the mobile manipulator and derive the dynamical model by using the Newton–Euler method, where a model which simultaneously takes account of features of both the manipulator and the mobile parts is given to analyze the effect of the movement of mounted manipulator on the platform. Then, the computed torque control and the resolved acceleration control methods are used to show that the holonomic omnidirectional mobile manipulator can be controlled so as to retain any end-effector position and orientation, irrespective of the direction of external applied force. The validity of the model and the effectiveness of the present mobile manipulator are proved by using several numerical simulations and 3D animations.     

Collaborative Multi-MSA Multi-Target Tracking and Surveillance: a Divide &; Conquer Method Using Region Allocation Trees

This work deals with the problem of the accurate task space control subject to finite-time convergence. Kinematic and dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, unbounded disturbances, i.e., such structures of the modelling functions that are generally not bounded by construction, are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous (chattering-free) robust controllers based on the estimation of a Jacobian transpose matrix, which seem to be effective in counteracting uncertain both kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a 2DOF robotic manipulator with two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.     

Elastic roadmaps—motion generation for autonomous mobile manipulation

The autonomous execution of mobile manipulation tasks in unstructured, dynamic environments requires the consideration of various motion constraints. The task itself imposes constraints, of course, but so do the kinematic and dynamic limitations of the manipulator, unpredictably moving obstacles, and the global connectivity of the workspace. All of these constraints need to be updated continuously in response to sensor feedback. We present the elastic roadmap framework, a novel feedback motion planning approach capable of satisfying all of these motion constraints and their respective feedback requirements. This framework is validated in simulation and real-world experiments using a mobile manipulation platform and a stationary manipulator.     

Collision‐free control of robotic manipulators in the task space

This paper addresses the problem of position control of robotic manipulators in the task space with obstacles. A computationally simple class of task space regulators consisting of a transpose Jacobian controller plus an integral term including the task error and the gradient of a penalty function generated by obstacles is proposed. The Lyapunov stability theory is used to derive the control scheme. Through the use of the exterior penalty function approach, collision avoidance of the robot with obstacles is ensured. The performance of the proposed control strategy is illustrated through computer simulations for a direct‐drive arm of a SCARA type manipulator operating in both an obstacle‐free task space and a task space including obstacles. © 2005 Wiley Periodicals, Inc.     

The SDRE control of mobile base cooperative manipulators: Collision free path planning and moving obstacle avoidance

This work proposes application of a state-dependent Riccati equation (SDRE) controller for wheeled mobile cooperative manipulators. Implementation of the SDRE on a wheeled mobile manipulator (WMM) considering holonomic and non-holonomic constraints is difficult and leads to instability of the system. The present study introduces a method of controlling the WMMs including: a general formulation, state-dependent coefficient parameterization, and control structure of the SDRE. Overcoming the problem of instability of the WMM resulted in control design for a system of cooperative manipulators mounted on a wheeled mobile platform. Optimal load distribution (OLD) was employed to distribute the load between the cooperative arms. The presence of obstacles and the probability of a collision between multiple robots in a workspace are the motivations behind employment of the artificial potential field (APF) approach. Two cooperative manipulators mounted on a mobile platform retrieved from Scout robot were modeled and simulated for situations such as controlling multiple mobile bases (collision avoidance), a cooperative system of manipulators, and moving obstacle avoidance. The OLD improved the load capacity, precision, and stability in motion of the cooperative system. Compatibility of the APF within the structure of the SDRE controller is another promising aspect of this research.     

Optimal Motion Planning of Robotic Manipulators Removing Mobile Objects Grasped in Motion

The following study deals with motion optimization of robot arms having to transfer mobile objects grasped when moving. This approach is aimed at performing repetitive transfer tasks at a rapid rate without interrupting the dynamics of both the manipulator and the moving object. The junction location of the robot gripper with the object, together with grasp conditions, are partly defined by a set of local constraints. Thus, optimizing the robot motion in the approach phase of the transfer task leads to the statement of an optimal junction problem between the robot and the moving object. This optimal control problem is characterized by constrained final state and unknown traveling time. In such a case, Pontryagin"s maximum principle is a powerful mathematical tool for solving this optimization problem. Three simulated results of removing a mobile object on a conveyor belt are presented; the object is grasped in motion by a planar three-link manipulator.     

基于状态空间的机械臂轨迹规划

提出一种基于状态空间的机械臂轨迹规划方法,定义并构造了机械臂系统的状态空间,根据内在机构约束与外部环境约束描述出系统状态的可达范围,并给出了任务的可实现条件.对于可实现任务,在状态空间能搜索到任务完成的最优解.如果任务无法完成,则修改系统配置或约束,在新的状态空间确定任务实现的转化条件,并对任务的设计与规划给予指导.研究了障碍约束下两连杆机械臂的点到点任务,实验结果验证了该方法的有效性.     

Constraint finite‐time control of redundant manipulators

This work addresses the problem of the accurate task‐space control subject to finite‐time convergence. Dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end effector. Furthermore, the movement is to be accomplished in such a way as to optimize some performance index. Based on suitably defined task‐space non‐singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of inverse‐free robust controllers consisting of a Jacobian transpose component plus a compensating term, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a Selective Compliant Articulated Robot for Assembly (SCARA) type consisting of three revolute kinematic pairs and operating in a two‐dimensional task space illustrate performance of the proposed controllers. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust adaptive control of uncertain force/motion constrained nonholonomic mobile manipulators

In this paper, force/motion tracking control is investigated for nonholonomic mobile manipulators with unknown parameters and disturbances under uncertain holonomic constraints. The nonholonomic mobile manipulator is transformed into a reduced chained form, and then, robust adaptive force/motion control with hybrid variable signals is proposed to compensate for parametric uncertainties and suppress bounded disturbances. The control scheme guarantees that the outputs of the dynamic system track some bounded auxiliary signals, which subsequently drive the kinematic system to the desired trajectory/force. Simulation studies on the control of a wheeled mobile manipulator are used to show the effectiveness of the proposed scheme.     

Weighted hierarchical quadratic programming: assigning individual joint weights for each task priority

This paper proposes a novel method that computes the optimal solution of the weighted hierarchical optimization problem for both equality and inequality tasks. The method is developed to resolve the redundancy of robots with a large number of Degrees of Freedom (DoFs), such as a mobile manipulator or a humanoid, so that they can execute multiple tasks with differently weighted joint motion for each priority level. The proposed method incorporates the weighting matrix into the first-order optimality condition of the optimization problem and leverages an active-set method to handle equality and inequality constraints. In addition, it is computationally efficient because the solution is calculated in a weighted joint space with symmetric null-space projection matrices for propagating recursively to a low priority task. Consequently, robots that utilize the proposed method effectively show whole-body motions handling prioritized tasks with differently weighted joint spaces. The effectiveness of the proposed method was validated through experiments with a nonholonomic mobile manipulator as well as a humanoid.

     

基于遗传算法的机械臂实时避障路径规划研究

针对模块化机械臂在运行时可能与工作空间中的障碍物发生碰撞的问题, 提出一种基于遗传算法的避障路径规划算法。首先采用D-H(Denavit-Hartenberg)表示法对机械臂进行建模, 并进行运动学和动力学分析, 建立机械臂运动学和动力学方程。在此基础上, 利用遗传算法分别在单/多个障碍物工作环境中, 以运动的时间、移动的空间距离和轨迹长度作为优化指标, 实现机械臂避障路径规划的优化。通过仿真验证了基于遗传算法的机械臂避障路径规划算法的有效性与可行性, 该算法提高了运行中的机械臂有效避开工作空间中障碍物的效率。