Cartesian control of redundant robots

This article presents a Cartesian-space position/force controller for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F ? R ^m and robot actuator torque T ? R ⁿ(for redundant robots, m < n). The underdetermined nature of the F → T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F → T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F→T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Obstacle avoidance for redundant robots using configuration control

The article presents a new and simple solution to the obstacle avoidance problem for redundant robots. In the proposed approach, called configuration control, the redundancy is utilized to configure the robot so as to satisfy a set of kinematic inequality constraints representing obstacle avoidance, while the end-effector is tracking a desired trajectory. The robot control scheme is very simple, and uses on-line adaptation to eliminate the need for the complex dynamic model and parameter values of the robot. Several simulation results for a four-link planar robot are presented to illustrate the versatility of the approach. These include reaching around a stationary obstacle, simultaneous avoidance of two obstacles, robot reconfiguration to avoid a moving obstacle, and avoidance of rectangular obstacles. The simplicity and computational efficiency of the proposed scheme allows on-line implementation with a high sampling rate for real-time obstacle avoidance in a dynamically varying environment.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

Localized online learning-based control of a soft redundant manipulator under variable loading

ABSTRACT

Soft robots are inherently compliant and manoeuvrable manipulators that can passively adapt to their environment. However, in order to fully make use of their unique properties, accurate control should still be maintained when affected by external loading. Commonly used model-based approaches often have low tolerance to unmodelled loading, resulting in significant error when acted on by them. Therefore, in this study we employ a nonparametric learning-based method that can approximate and update the inverse model of a redundant two-segment soft robot in an online manner. The primary contribution of this work is the application and evaluation of the proposed framework on a redundant soft robot. With the addition of redundancy, a constrained optimization approach is taken to consistently resolve null-space behaviour. Through this control framework, the controller can continuously adapt to unknown external disturbances during runtime and maintain end-effector accuracy. The performance of the control framework was evaluated by tracking of a 3D trajectory with a static tip load, and a variable weight tip load. The results indicate that the proposed controller could effectively adapt to the disturbances and continue to track the desired trajectory accurately.     

Mobile robot characterized by dynamic and kinematic equations and actuator dynamics: Trajectory tracking and related application

This paper establishes control strategies for wheeled mobile robots which are subjected to nonholonomic constraints. The mobile robot model includes the kinematic and dynamic equations of motion and the actuator dynamics. Using the notion of virtual vehicle and the concept of flatness, and applying the backstepping methodology the paper proposes control schemes for trajectory tracking for the considered augmented model of the mobile robot. The resulting controller ensures exponential convergence to a desired trajectory. Applications of the tracking controller for convoy-like vehicles governed by the augmented models are considered as well. Simulation results and lab experiments are demonstrated.     

Criteria optimization using self-motion of a 9-R redundant robot

Using inverse kinematic solutions for self-motion of a class of 9-R redundant robots, a conjugate-gradient based constrained optimization scheme for incremental trajectory planning is formulated. The proposed scheme has been evaluated and proved to be an efficient optimization method for redundancy utilization. It can also be used for studying 7-R and 8-R manipulators by simply restricting to one-variable and two-variable optimization, respectively. In contrast with other approaches which are based on the Jacobian, our scheme exploits the availability of closed-form inverse kinematic solutions to give more effective and accurate results.     

Adaptive Jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models

Most research so far on robot trajectory control has assumed that the kinematics of the robot is known exactly. However, when a robot picks up tools of uncertain lengths, orientations, or gripping points, the overall kinematics becomes uncertain and changes according to different tasks. Recently, we derived a new adaptive Jacobian tracking controller for robots with uncertain kinematics and dynamics. This note extends the results to include redundant robots and adaptation to actuator parameters. Experimental results are presented to illustrate the performance of the proposed controller.     

Joint trajectory generation for redundant robots in an environment with obstacles

Collision avoidance is an absolutely essential requirement for a robot to complete a task in an environment with obstacles. For kinematically redundant robots, collision avoidance can be achieved by making full use of the redundancy. In this article, the problem of determining collision-free joint space trajectories for redundant robots in an environment with multiple obstacles is considered, and the “command generator” approach is employed to generate such trajectories. In this approach, a nondifferentiable distance objective function is defined and is guaranteed to increase wherever possible along the trajectory through a vector in N(J), the null space of Jacobian matrix J. Algorithms that implement this nondifferentiable optimization problem are fully developed. It is shown that the proposed collision-free trajectory generation scheme is efficient and practical. Extensive simulation results of a four-link robot example are presented and analyzed.     

A recurrent neural network for minimum infinity-norm kinematiccontrol of redundant manipulators with an improved problem formulationand reduced architecture complexity

This paper presents an improved neural computation where scheme for kinematic control of redundant manipulators based on infinity-norm joint velocity minimization. Compared with a previous neural network approach to minimum infinity-non kinematic control, the present approach is less complex in terms of cost of architecture. The recurrent neural network explicitly minimizes the maximum component of the joint velocity vector while tracking a desired end-effector trajectory. The end-effector velocity vector for a given task is fed into the neural network from its input and the minimum infinity-norm joint velocity vector is generated at its output instantaneously. Analytical results are given to substantiate the asymptotic stability of the recurrent neural network. The simulation results of a four-degree-of-freedom planar robot arm and a seven-degree-of-freedom industrial robot are presented to show the proposed neural network can effectively compute the minimum infinity-norm solution to redundant manipulators.     

Adaptive control of free-floating space robots in Cartesian coordinates

An adaptive control scheme is proposed for the end-effector trajectory tracking control of free-floating space robots. In order to cope with the nonlinear parameterization problem of the dynamic model of the free-floating space robot system, the system is modeled as an extended robot which is composed of a pseudo-arm representing the base motions and a real robot arm. An on-line estimation of the unknown parameters along with a computed-torque controller is used to track the desired trajectory. The proposed control scheme does not require measurement of the accelerations of the base and the real robot arm. A two-link planar space robot system is simulated to illustrate the validity and effectiveness of the proposed control scheme.     

提高柔性冗余度机器人动态特性的最小变形能法

冗余度柔性机器人的运动规划是机器人领域的重要前沿课题之一 .利用此机器人的冗余特性 ,可以改善其运动学和动力学性能 .柔性机器人的变形能能够很好地反映出其整体弹性变形程度 .本文提出了在最小变形能意义下的柔性冗余度机器人运动学规划的新方法 .以平面三柔性臂机器人为例进行了仿真 ,通过与最小末端误差意义下的规划策略进行比较 ,充分显示了最小变形能法在提高柔性机器人动态性能的有效性和优越性     

含驱动器动力学的移动机器人编队自适应控制

针对含有驱动器及编队动力学的多非完整移动机器人编队控制问题,基于领航者-跟随者[l-ψ]控制结构,通过反步法设计了一种将运动学控制器与驱动器输入电压控制器相结合的新型控制策略。采用径向基神经网络（RBFNN）对跟随者及领航者动力学非线性不确定部分进行在线估计,并通过自适应鲁棒控制器对神经网络建模误差进行补偿。该方法不但解决了移动机器人编队控制的参数与非参数不确定性问题,同时也确保了机器人编队在期望队形下对指定轨迹的跟踪;基于Lyapunov方法的设计过程,保证了控制系统的稳定与收敛;仿真结果表明了该方法的有效性。     

Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator

This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator for solving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forward network such as a radial basis function (RBF) network is used to learn the forward kinematic map of the redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until the network inversion solution guides the manipulator end-effector to reach a given target position with a specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme, depends on the approximation error present in the forward model. But, an accurate forward map would require a very large size of training data as well as network architecture. The proposed inverse-forward adaptive scheme effectively approximates the forward map around the joint angle vector provided by a hint generator. Thus the inverse kinematic solution obtained using the network inversion approach can take the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithm with an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable of providing multiple hints. This problem has been addressed by using a Kohonen self organizing map based sub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting a suitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCube? manipulator. It is shown that one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even when the forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solved to demonstrate the redundancy resolution process with the proposed scheme.     

Robust adaptive control of redundant manipulators

This paper presents an adaptive scheme for the motion control of kinematically redundant manipulators. The proposed controller is very general and computationally efficient since it does not require knowledge of either the mathematical model or the parameter values of the robot dynamics, and is implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategy is globally stable in the presence of bounded disturbances, and that in the absence of disturbances the size of the residual tracking errors can be made arbitrarily small. The performance of the controller is illustrated through computer simulations with a nine degree-of-freedom (DOF) compound manipulator consisting of a relatively small, fast six-DOF manipulator mounted on a large three-DOF positioning device. These simulations demonstrate that the proposed scheme provides accurate and robust trajectory tracking and, moreover, permits the available redundancy to be utilized so that a high bandwidth response can be achieved over a large workspace.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.     

Global Output Tracking Control of Flexible Joint Robots via Factorization of the Manipulator Mass Matrix

This paper investigates the problem of global output feedback tracking control of flexible joint robots. Despite the fact that only link position and actuator position are available from measurements, the proposed controller ensures that the link position globally tracks the desired trajectory while keeping all the remaining signals bounded. The controller development uses a partial state-feedback linearization technique combined with the integrator backstepping control design method whereas a filter and an observer are utilized to remove the requirement of link and actuator velocity measurements. Partial state-feedback linearization of robot dynamics is performed by factoring the manipulator mass matrix into a quadratic form involving an integrable root matrix. The applicability of the proposed general design methodology is illustrated by an example of flexible joint planar robots. Numerical results for a two-link flexible joint planar robot are also provided.      

A real-time planning algorithm for obstacle avoidance of redundant robots

A computationally efficient, obstacle avoidance algorithm for redundant robots is presented in this paper. This algorithm incorporates the neural networks and pseudodistance function D _p in the framework of resolved motion rate control. Thus, it is well suited for real-time implementation. Robot arm kinematic control is carried out by the Hopfield network. The connection weights of the network can be determined from the current value of Jacobian matrix at each sampling time, and joint velocity commands can be generated from the outputs of the network. The obstacle avoidance task is achieved by formulating the performance criterion as D _p>d _min (d _min represents the minimal distance between the redundant robot and obstacles). Its calculation is only related to some vertices which are used to model the robot and obstacles, and the computational times are nearly linear in the total number of vertices. Several simulation cases for a four-link planar manipulator are given to prove that the proposed collision-free trajectory planning scheme is efficient and practical.     

Model-based control of redundantly actuated parallel manipulators in redundant coordinates

Model-based control of parallel kinematics machines (PKM) relies on computationally efficient formulations in terms of a set of independent joint coordinates. Since PKM models are commonly expressed in terms of actuator or end-effector coordinates the models are not valid at input- or output-singularities, respectively. Moreover input-singularities limit the motion range of PKM. Actuation redundancy is a means to increase the singularity-free range of motion. However, due to the redundancy only a subset of the actuator coordinates constitute independent coordinates. This subset corresponds to the actuator coordinates of the non-redundant PKM, which does generally not constitute proper minimal coordinates for the entire workspace. Hence a redundantly actuated PKM (RA-PKM) controlled by a model-based controller in terms of minimal coordinates would exhibit the same limitations as the non-redundant PKM. One approach to tackle this problem is to switch between different minimal coordinates, i.e., different motion equations are used within the controller.In this contribution a computed torque and augmented PD control scheme in redundant coordinates is proposed, as an alternative to coordinate switching, and applied to the control of redundantly actuated PKM. That is, no minimal coordinates are selected. This novel formulation is numerically robust and does not suffer from input- or output-singularities. Even more the formulation is always valid except at configuration space singularities. For the redundancy resolution within the inverse dynamics the pseudoinverse of a rank deficient matrix is required, for which an explicit formulation is presented. For both controllers exponential trajectory tracking is shown. Experimental results are reported for a planar 2 DOF RA-PKM.