Handling robot constraints within a Set-Based Multi-Task Priority Inverse Kinematics Framework

Set-Based Multi-Task Priority is a recent framework to handle inverse kinematics for redundant structures. Both equality tasks, i.e., control objectives to be driven to a desired value, and set-bases tasks, i.e., control objectives to be satisfied with a set/range of values can be addressed in a rigorous manner within a priority framework. In addition, optimization tasks, driven by the gradient of a proper function, may be considered as well, usually as lower priority tasks. In this paper the proper design of the tasks, their priority and the use of a Set-Based Multi-Task Priority framework is proposed in order to handle several constraints simultaneously in real-time. It is shown that safety related tasks such as, e.g., joint limits or kinematic singularity, may be properly handled by consider them both at an higher priority as set-based task and at a lower within a proper optimization functional. Experimental results on a 7DOF Jaco$^2

On-line Joint Limit Avoidance for Torque Controlled Robots by Joint Space Parametrization

This paper proposes control laws ensuring the stabilization of a time-varying desired joint trajectory, as well as joint limit avoidance, in the case of fully-actuated manipulators. The key idea is to perform a parametrization of the feasible joint space in terms of exogenous states. It follows that the control of these states allows for joint limit avoidance. One of the main outcomes of this paper is that position terms in control laws are replaced by parametrized terms, where joint limits must be avoided. Stability and convergence of time-varying reference trajectories obtained with the proposed method are demonstrated to be in the sense of Lyapunov. The introduced control laws are verified by carrying out experiments on two degrees-of-freedom of the humanoid robot iCub.Comment: 8 pages, 4 figures. Submitted to the 2016 IEEE-RAS International Conference on Humanoid Robot

Position-based kinematics for 7-DoF serial manipulators with global configuration control, joint limit and singularity avoidance

This paper presents a novel analytic method to uniquely solve inverse kinematics of 7 degrees-of-freedom manipulators while avoiding joint limits and singularities. Two auxiliary parameters are introduced to deal with the self-motion manifolds: the global configuration (GC), which specifies the branch of inverse kinematics solutions; and the arm angle (ψ) that parametrizes the elbow redundancy within the specified branch. The relations between the joint angles and the arm angle are derived, in order to map the joint limits and singularities to arm angle values. Then, intervals of feasible arm angles for the specified target pose and global configuration are determined, taking joint limits and singularities into account. A simple metric is proposed to compute the elbow position according to the feasible intervals. When the arm angle is determined, the joint angles can be uniquely calculated from the position-based inverse kinematics algorithm. The presented method does not exhibit the disadvantages inherent to the use of the Jacobian matrix and can be implemented in real-time control systems. This novel algorithm is the first position-based inverse kinematics algorithm to solve both global and local manifolds, using a redundancy resolution strategy to avoid singularities and joint limits.This work was partially supported by the NETT Project [FP7-PEOPLE-2011-ITN-289146]; and Foundation for Science and Technology, Portugal [grant number SFRH/BD/86499/2012].info:eu-repo/semantics/publishedVersio

Self-motion control of kinematically redundant robot manipulators

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 88-92)Text in English; Abstract: Turkish and Englishxvi,92 leavesRedundancy in general provides space for optimization in robotics. Redundancy can be defined as sensor/actuator redundancy or kinematic redundancy. The redundancy considered in this thesis is the kinematic redundancy where the total degrees-of-freedom of the robot is more than the total degrees-of-freedom required for the task to be executed. This provides infinite number of solutions to perform the same task, thus, various subtasks can be carried out during the main-task execution. This work utilizes the property of self-motion for kinematically redundant robot manipulators by designing the general subtask controller that controls the joint motion in the null-space of the Jacobian matrix. The general subtask controller is implemented for various subtasks in this thesis. Minimizing the total joint motion, singularity avoidance, posture optimization for static impact force objectives, which include maximizing/minimizing the static impact force magnitude, and static and moving obstacle (point to point) collision avoidance are the subtasks considered in this thesis. New control architecture is developed to accomplish both the main-task and the previously mentioned subtasks. In this architecture, objective function for each subtask is formed. Then, the gradient of the objective function is used in the subtask controller to execute subtask objective while tracking a given end-effector trajectory. The tracking of the end-effector is called main-task. The SCHUNK LWA4-Arm robot arm with seven degrees-of-freedom is developed first in SolidWorks® as a computer-aided-design (CAD) model. Then, the CAD model is converted to MATLAB® Simulink model using SimMechanics CAD translator to be used in the simulation tests of the controller. Kinematics and dynamics equations of the robot are derived to be used in the controllers. Simulation test results are presented for the kinematically redundant robot manipulator operating in 3D space carrying out the main-task and the selected subtasks for this study. The simulation test results indicate that the developed controller’s performance is successful for all the main-task and subtask objectives

Method and apparatus for configuration control of redundant robots

A method and apparatus to control a robot or manipulator configuration over the entire motion based on augmentation of the manipulator forward kinematics is disclosed. A set of kinematic functions is defined in Cartesian or joint space to reflect the desirable configuration that will be achieved in addition to the specified end-effector motion. The user-defined kinematic functions and the end-effector Cartesian coordinates are combined to form a set of task-related configuration variables as generalized coordinates for the manipulator. A task-based adaptive scheme is then utilized to directly control the configuration variables so as to achieve tracking of some desired reference trajectories throughout the robot motion. This accomplishes the basic task of desired end-effector motion, while utilizing the redundancy to achieve any additional task through the desired time variation of the kinematic functions. The present invention can also be used for optimization of any kinematic objective function, or for satisfaction of a set of kinematic inequality constraints, as in an obstacle avoidance problem. In contrast to pseudoinverse-based methods, the configuration control scheme ensures cyclic motion of the manipulator, which is an essential requirement for repetitive operations. The control law is simple and computationally very fast, and does not require either the complex manipulator dynamic model or the complicated inverse kinematic transformation. The configuration control scheme can alternatively be implemented in joint space

Robust adaptive kinematic control of redundant robots

The paper presents a general method for the resolution of redundancy that combines the Jacobian pseudoinverse and augmentation approaches. A direct adaptive control scheme is developed to generate joint angle trajectories for achieving desired end-effector motion as well as additional user defined tasks. The scheme ensures arbitrarily small errors between the desired and the actual motion of the manipulator. Explicit bounds on the errors are established that are directly related to the mismatch between actual and estimated pseudoinverse Jacobian matrix, motion velocity and the controller gain. It is shown that the scheme is tolerant of the mismatch and consequently only infrequent pseudoinverse computations are needed during a typical robot motion. As a result, the scheme is computationally fast, and can be implemented for real-time control of redundant robots. A method is incorporated to cope with the robot singularities allowing the manipulator to get very close or even pass through a singularity while maintaining a good tracking performance and acceptable joint velocities. Computer simulations and experimental results are provided in support of the theoretical developments

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

Local performance optimization for a class of redundant eight-degree-of-freedom manipulators

Local performance optimization for joint limit avoidance and manipulability maximization (singularity avoidance) is obtained by using the Jacobian matrix pseudoinverse and by projecting the gradient of an objective function into the Jacobian null space. Real-time redundancy optimization control is achieved for an eight-joint redundant manipulator having a three-axis spherical shoulder, a single elbow joint, and a four-axis spherical wrist. Symbolic solutions are used for both full-Jacobian and wrist-partitioned pseudoinverses, partitioned null-space projection matrices, and all objective function gradients. A kinematic limitation of this class of manipulators and the limitation's effect on redundancy resolution are discussed. Results obtained with graphical simulation are presented to demonstrate the effectiveness of local redundant manipulator performance optimization. Actual hardware experiments performed to verify the simulated results are also discussed. A major result is that the partitioned solution is desirable because of low computation requirements. The partitioned solution is suboptimal compared with the full solution because translational and rotational terms are optimized separately; however, the results show that the difference is not significant. Singularity analysis reveals that no algorithmic singularities exist for the partitioned solution. The partitioned and full solutions share the same physical manipulator singular conditions. When compared with the full solution, the partitioned solution is shown to be ill-conditioned in smaller neighborhoods of the shared singularities

Redundancy analysis of cooperative dual-arm manipulators

This paper presents the redundancy analysis of two cooperative manipulators, showing how they can be considered as a single redundant manipulator through the use of the relative Jacobian matrix. In this way, the kinematic redundancy can be resolved by applying the principal local optimization techniques used in the single manipulator case. We resolve the redundancy by using the Jacobian null space technique, which permits us to perform several tasks with different execution priority levels at the same time; this is a useful feature, especially when the manipulators are to be mounted on and cooperate with a mobile platform. As an illustrative example, we present a case study consisting of two planar manipulators mounted on a smart wheelchair, whose degrees of redundancy are employed to move an object along a pre-defined path, while avoiding an obstacle in the manipulator's workspace at the same time