Redundancy Resolution Scheme Research Articles

Stabilization and control on a pipe-rack of a wheeled mobile manipulator with a snake-like arm

Autonomous inspection and maintenance tasks with robots in oil and gas refineries require moving along pipelines and manipulation dexterity in cluttered environments. This paper investigates the problem of controlling a wheeled mobile manipulator endowed with a snake-like arm to inspect the structures while stabilizing the supporting pipe. A model predictive control approach stabilizes the wheeled robot on the pipe. When the wheel torques saturate, the stabilization task leverages the resulting propagating force on the wheeled robot given by the snake-like arm’s dynamics. The significant number of degrees of freedom given by the snake-like arm allows a prioritized redundancy resolution scheme with hybrid motion/force tracking to inspect the same and adjacent pipes while avoiding self-collisions and environmental impacts. Simulations in the realistic Gazebo environment validate the achieved preliminary results.

Cable failure tolerant control and planning in a planar reconfigurable cable driven parallel robot.

The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations.

Redundancy Resolution Scheme for Manipulators Subject to Inequality Constraints

Redundancy Resolution Scheme for Manipulators Subject to Inequality Constraints

Human-like redundancy resolution: An integrated inverse kinematics scheme for anthropomorphic manipulators with radial elbow offset

As a mimic of the human arm structure, anthropomorphic manipulators with radial elbow offset (AMREO) are often deployed on humanoid service robots. However, the unique offset leads to difficulties in solving the analytical inverse kinematics (IK), which poses a challenge for further anthropomorphic control. This paper presents an integrated scheme for solving the path-wise IK problem of a 7-DoF AMREO in the position domain. Unlike other approaches, special attention is paid to the naturalness of the arm configuration, with the aim of making AMREO exhibit human-like behavior in human-centered environments. First, an analytical IK solution of AMREO for a single end-effector pose is derived based on the arm angle parameterization. Then, inspired by the habitual arm configurations in human reaching movements, the natural arm configuration mapped to wrist position is proposed for AMREO. To learn the patterns implied therein, a LSTM-based natural arm angle prediction network (NAPN) is designed and trained based on a human demonstration dataset. Finally, a redundancy resolution framework embedded with NAPN is built to generate smooth and natural joint configurations in the path-wise IK tasks. Comparative experiments show that the proposed analytical IK algorithm has better computational efficiency and precision than conventional methods, and can give complete results for one IK call within 4 μs. In addition, continuous path tracking experiments on a real robot validate the effectiveness and anthropomorphism of the redundancy resolution scheme based on NAPN.

Model-based recurrent neural network for redundancy resolution of manipulator with remote centre of motion constraints

Redundancy resolution is a critical issue to achieve accurate kinematic control for manipulators. End-effectors of manipulators can track desired paths well with suitable resolved joint variables. In some manipulation applications such as selecting insertion paths to thrill through a set of points, it requires the distal link of a manipulator to translate along such fixed point and then perform manipulation tasks. The point is known as remote centre of motion (RCM) to constrain motion planning and kinematic control of manipulators. Together with its end-effector finishing path tracking tasks, the redundancy resolution of a manipulators has to maintain RCM to produce reliable resolved joint angles. However, current existing redundancy resolution schemes on manipulators based on recurrent neural networks (RNNs) mainly are focusing on unrestricted motion without RCM constraints considered. In this paper, an RNN-based approach is proposed to solve the redundancy resolution issue with RCM constraints, developing a new general dynamic optimisation formulation containing the RCM constraints. Theoretical analysis shows the theoretical derivation and convergence of the proposed RNN for redundancy resolution of manipulators with RCM constraints. Simulation results further demonstrate the efficiency of the proposed method in end-effector path tracking control under RCM constraints based on an industrial redundant manipulator system.

Model-based joint and task space control strategies for a kinematically redundant parallel manipulator

AbstractOne alternative to overcome the presence of singularities within Parallel Manipulators’ workspace is kinematic redundancy. This design alternative can be realized by adding an extra active joint to a kinematic chain. Due to this addition, the IKM presents an infinite number of solutions requiring a redundancy resolution scheme. Moreover, Parallel Manipulators’ control may require complex strategies due to their coupled and complex dynamic and kinematic relations. In this work, a model-free, a joint space computed torque, and a hybrid joint-task-space computed torque control strategies are experimentally compared for a kinematically redundant parallel manipulator. The latter is a novel strategy that requires the measurement of the end-effector’s pose, which is performed by an eye-to-hand limited frame rate camera. The impact of up to three kinematic redundancy levels is also experimentally evaluated using prepositioning and ongoing positioning redundancy resolution schemes. The data are assessed by evaluating a prescribed trajectory executed using a planar kinematically redundant parallel manipulator. These results indicate that kinematic redundancy can not only be used as an alternative design for reducing the presence of singular regions, as claimed in the literature, but also be used along with model-based control strategies for improving dynamic performance and accuracy of parallel manipulators.

An effort for resolving redundancy of a multi-finger robotic hand in straight-line motions

Multi-finger robotic hands are the main robotic invention for providing assistive movement therapy in hand rehabilitation. In this paper, the concept of task priority is adopted in order to solve the redundancy resolution of a robotic hand. The redundancy parameter has been used to design the inverse kinematic model in order to determine the joint angles when the finger moves to perform the initial subtask of tracing the desired trajectory while considering the secondary subtask of increasing the instantaneous manipulability. Five different human subjects performed the experimentation where the index finger and thumb are allowed to follow the three desired motion trajectories. Markers are placed on the finger joints in order to track the motion and obtain the finger joint angles. Further, the experimental joint angles are compared with those obtained from inverse kinematics. The index finger and thumb behaviour is analysed based on the redundancy resolution scheme. It has been observed that the optimized root-mean-square error remains insignificant of the different subjects performing the motion and the type of motion trajectories adopted for the index finger as well as the thumb. Thereafter, the proposed scheme is applied to a four-finger tendon-actuated robotic hand and it has been observed that the scheme can be applied to solve the redundancies of any robotic hand.

Investigating the potential of redundant manipulators in narrow channels

In this paper, an attempt has been made to investigate the potential of redundant manipulators, while tracking trajectories in narrow channels. The behavior of redundant manipulators is important in many challenging applications like under-water welding in narrow tanks, checking the blockage in sewerage pipes, performing a laparoscopy operation etc. To demonstrate this snake-like behavior, redundancy resolution scheme is utilized using two different approaches. The first approach is based on the concept of task priority, where a given task is split and prioritize into several subtasks like singularity avoidance, obstacle avoidance, torque minimization, and position preference over orientation etc. The second approach is based on Adaptive Neuro Fuzzy Inference System (ANFIS), where the training is provided through given datasets and the results are back-propagated using augmentation of neural networks with fuzzy logics. Three case studies are considered in this work to demonstrate the redundancy resolution of serial manipulators. The first case study of 3-link manipulator is attempted with both the approaches, where the objective is to track the desired trajectory while avoiding multiple obstacles. The second case study of 7-link manipulator, tracking trajectory in a narrow channel, is investigated using the concept of task priority. The realistic application of minimum-invasive surgery (MIS) based trajectory tracking is considered as the third case study, which is attempted using ANFIS approach. The 5-link spatial redundant manipulator, also known as a patient-side manipulator being developed at CSIR-CSIO, Chandigarh is used to track the desired surgical cuts. Through the three case studies, it is well demonstrated that both the approaches are giving satisfactory results.

On the Optimal Resolution of Inverse Kinematics for Redundant Manipulators Using a Topological Analysis

Abstract The redundancy resolution schemes based on the optimization of an integral performance index are investigated from the topological point of view. The topological notions of self-motion manifold, C-path-homotopy and extended aspect are clarified in relation to the limitations of the necessary conditions of optimality provided by calculus of variations. On one hand, they do not guarantee the achievement of the optimal solution, and on the other hand, they translate into a two-point boundary value problem (TPBVP), whose resolution, under certain circumstances, may not lead to a feasible solution at all. In response to the limitations of calculus of variations, a dynamic-programming-inspired formalism is developed, which is based on the discretization of the state space and on its representation in the form of multiple grids. Building upon the topological analysis, effective algorithms are designed that are able to find the optimal solution in any condition, across all C-path homotopy classes and self-motion manifolds, with no limitation due to the passage through singularities. Moreover, if the grids are representative of the manipulator’s extended aspects, the topological notion of the transitional point can be used to reduce the computational complexity of the optimal redundancy resolution algorithm. The results are demonstrated on a canonical 4R planar robot in two different scenarios.

Recurrent-Neural-Network-Based Velocity-Level Redundancy Resolution for Manipulators Subject to a Joint Acceleration Limit

For the safe operation of redundant manipulators, physical constraints such as the joint angle, joint velocity, and joint acceleration limits should be taken into account when designing redundancy resolution schemes. Velocity-level redundancy resolution schemes are widely adopted in the kinematic control of redundant manipulators due to the existence of the well-tuned inner loop regarding the joint velocity control. However, it is difficult to deal with joint acceleration limits for velocity-level redundancy resolution methods. In this paper, a recurrent-neural-network-based velocity-level redundancy resolution method is proposed to deal with the problem, and theoretical results are given to guarantee its performance. By the proposed method, the end-effector position error is asymptotically convergent to zero, and all the joint limits are not violated. The effectiveness and superiority of the proposed scheme are validated via simulation results.

The Application of Noise-Tolerant ZD Design Formula to Robots’ Kinematic Control via Time-Varying Nonlinear Equations Solving

Recently, a new formula with noise-tolerant capability has been designed by Zhang et al. , and the resultant Zhang dynamics (ZD) models have been developed to solve different types of time-varying problems. Based on previous research, this paper presents and investigates the application of such a noise-tolerant ZD design formula to kinematic control of redundant robot manipulators via time-varying nonlinear equations solving. Specifically, by exploiting this ZD design formula to solve the system of time-varying nonlinear kinematic equations involved in robot control, the redundancy-resolution scheme is established. Such a scheme contains the proportional, integral, and derivative information of the desired Cartesian path of the robot end-effector and can thus be viewed as a nonlinear proportional-integral-derivative controller for redundant robot manipulators. Then, theoretical results are given to show that the redundancy-resolution scheme has the capability of noise suppressing. Simulation results based on a four-link planar robot manipulator and a PA10 robot manipulator with zero, constant, and bounded time-varying noises further substantiate the efficacy and superiority of the redundancy-resolution scheme, and show the application prospect of the noise-tolerant ZD design formula.

Velocity-Level Control With Compliance to Acceleration-Level Constraints: A Novel Scheme for Manipulator Redundancy Resolution

Manipulators are subject to physical constraints at different levels, i.e., joint angle limits, joint velocity limits, and acceleration limits. Effective resolution of redundant manipulators with compliance to the physical constraints is a fundamental issue for safe operation. Existing results generally resolve the manipulator redundancy either at the velocity level or the acceleration level. On the one hand, the velocity-level redundancy resolution scheme is able to deal with the joint angle and joint velocity limits successfully but cannot address the joint acceleration limit. On the other hand, although the existing acceleration-level redundancy resolution scheme is able to overcome the failure of the velocity-level one in complying with acceleration constraints, it is at the cost of making the system equation more complicated, e.g., the dependence on the time derivative of the Jacobian matrix. Whether it is possible to conduct redundancy resolution at the velocity level but with the compliance to joint angle constraints, joint velocity constraints, and joint acceleration constraints remains an open problem in past decades. This paper gives a positive answer to this pending problem by providing a novel scheme. In the proposed scheme, the redundancy resolution problem is formulated as a quadratic program subject to joint angle, velocity, and acceleration constraints with the joint velocity being the decision variable and joint velocity norm as the performance index, which is widely adopted and closely related to the energy consumption. Then, a projection neural network is designed and proposed to online solve the problem with the joint acceleration constraint handled. Theoretical analysis is performed to guarantee the global convergence of the proposed projection neural network to the optimal solution to the redundancy resolution problem. Besides, simulation results based on a PUMA 560 industrial manipulator are presented and compared to verify the theoretical result and substantiate the efficacy and superiority of the proposed scheme.

Numerical and experimental evaluation of the dynamic performance of kinematically redundant parallel manipulators

Parallel manipulators present high load capacity and rigidity, among other advantages, when compared to the serial manipulators. Due to their kinematic architecture, their parts are lighter. This characteristic may be an asset for designing high dynamic performance manipulators. However, parallel manipulators suffer from singularities in their workspace. This drawback can be circumvented by the use of kinematic redundancies. Due to the presence of these redundancies, the inverse kinematic problem presents an infinite number of solutions. The selection of a single solution among the possible ones is denoted as redundancy resolution. In this manuscript, the impact of several levels of kinematic redundancy on the dynamic performance of a planar parallel manipulator, the 3PRRR, is numerically and experimentally investigated. The kinematic redundancy of this manipulator can be added by the actuation of the active prismatic joints (P). Two redundancy resolution schemes are proposed using a multiobjective optimization problem. Based on the numerical and experimental results, one can conclude that the use of a proper redundancy resolution scheme can considerably reduce the maximum required torque to perform a predefined task.

On redundancy resolution and energy consumption of kinematically redundant planar parallel manipulators

SUMMARYNovel kinematic architectures can be alternatives for designing energy efficient robotic systems. In this work, the impact of kinematic redundancies in the energy consumption of a planar PKM, the 3PRRR manipulator, is experimentally verified. Because of the presence of the kinematic redundancies, the inverse kinematic problem presents infinity solutions. In this way, a redundancy resolution scheme based on the Model Predictive Control technique is proposed and exploited. It can be concluded that the energy consumption of the non-redundant parallel manipulator 3RRR for executing predefined tasks can be considerably reduced by the inclusion of kinematic redundancies.

Optimal robot placement with consideration of redundancy problem for wrist-partitioned 6R articulated robots

Abstract Rapid set-up of robotic system is critical for realising the high-mix low-volume applications. This paper presents an efficient method to determine the optimal robot base placement for executing required end-effector trajectories while dealing with redundancy problem for wrist-partitioned 6 R articulated robots. The main feature of the method includes the integration of two multi-objectives optimization loops that involve parameterized inverse kinematics of the robot to find the proper robot configurations. Firstly, an optimization scheme is introduced in consideration of all the robot and operational constraints including reachability, singularity avoidance, and collision avoidance. Then, a redundancy resolution scheme is proposed based on a modified particle swarm optimization (MPSO) for the considered target point. Consequently, the optimal robot base placement is obtained via another optimization loop which includes all robot trajectories for the application. The method was applied in a complex robotic welding application. For a set of desired welding torch trajectories on the workpiece, the optimal robot base placement is computed within a few minutes.

Efficient method for position control of a redundant robot

To begin the work presents some redundancy resolution schemes for robotic arms, i.e., the techniques for exploiting the redundant degrees of freedom in the solution of the inverse kinematics problem. This is obviously an issue of major relevance for motion planning and control purposes. In particular, task-oriented kinematics and the basic methods for its inversion at the velocity (first-order differential) level are first recalled. This paper focuses on modeling and simulations of the inverse kinematics of an anthropomorphic redundant robotic structure with seven degrees of freedom and a workspace similar to human arm. Also the kinematic model of the robotic arm in the MATLAB and Simulink environment is presented. A method of resolving the redundancy of a seven degrees of freedom robotic arm when a degree of freedom has a known variation is presented. The kinematic analysis and virtual simulation share similar results.

Revisit and compare Ma equivalence and Zhang equivalence of minimum velocity norm (MVN) type

In this paper, by revisiting Ma et al.’s inspiring work (specifically, Ma equivalence, ME) and Zhang et al.’s inspiring work (specifically, Zhang equivalence, ZE), which both investigate the equivalence relationships of redundancy-resolution schemes at two different levels, but with different formulations, the general scheme formulations and equivalence analyses of ME and ZE are presented. Besides, being a case study, the ME and ZE of minimum velocity norm (MVN) type are investigated for the inverse-kinematics (IK) problem solving. Moreover, the link and difference between the MVN-type ME and ZE are analyzed, summarized and presented methodologically, systematically, and computationally in this paper. In order to numerically compare the ME and ZE of MVN type, a Rhodonea-path tracking task based on PUMA560 robot manipulator is tested and fulfilled by employing the original velocity-level MVN schemes and its equivalent acceleration-level MVN schemes of ME and ZE. The simulative and numerical results not only verify the effectiveness of the velocity-level and acceleration-level schemes of MVN-type ME and ZE, but also validate the reasonableness of such two proved equivalence relationships. More importantly, these results show quantitatively and comparatively the respective advantages and future applications of MVN-type ME and ZE for the IK problem solving.

Task-space dynamics and motion/force control of fixed-base manipulators under reaction null-space-based redundancy resolution

SUMMARYThis paper introduces a task-space dynamics formulation for fixed-base serial-link kinematically redundant manipulators and a motion/force controller based on it. The aim is to alleviate joint-space instability problems that have been observed with other motion/force controllers. The dynamics are represented in floating-base coordinates, wherein the end effector is regarded as the floating base. This representation gives rise to a momentum-conserving redundancy resolution scheme based on the reaction null-space (RNS) method used in past studies on free-floating and flexible-base space robots. A generalized inverse is obtained that is shown to satisfy the conditions for dynamic consistency in the sense of the operational space (OS) formulation, but may lead to the joint-space instabilities observed earlier. The proposed controller is based on the pseudoinverse of the coupling inertia matrix and ensures reactionless link motion that does not disturb the force balance at the end effector. The performance of the RNS motion/force controller is examined by comparison to that with an OS motion/force controller. It is shown that while the performance in task-space of both controllers is satisfactory, the joint-space performance of the proposed controller is superior.

An off-line programming system for robotic drilling in aerospace manufacturing

Off-line programming systems are essential tools for the effective use of robots in the manufacturing environment. This paper presents a dedicated off-line programming system for robotic drilling in aerospace manufacturing. Following a brief introduction of the system architecture, the paper discusses two major problems of off-line programming for robotic drilling, i.e., redundancy resolution and position correction. A new performance index is proposed for the combined requirements of singularity and joint-limit avoidance, followed by a discussion of the redundancy resolution scheme by using numerical optimization at the joint displacement level. A position correction method using measurement data of reference holes is developed for the enhancement of robotic drilling accuracy. Robot programs generated by using the developed system have been tested on a robotic drilling system, and the experimental results are provided.

Different-Level Redundancy-Resolution and Its Equivalent Relationship Analysis for Robot Manipulators Using Gradient-Descent and Zhang 's Neural-Dynamic Methods

To solve the inverse kinematic problem of redundant robot manipulators, two redundancy-resolution schemes are investigated: one is resolved at joint-velocity level, and the other is resolved at joint-acceleration level. Both schemes are reformulated as a quadratic programming (QP) problem. Two recurrent neural networks (RNNs) are then developed for the online solution of the resultant QP problem. The first RNN solver is based on the gradient-descent method and is termed as gradient neural network (GNN). The other solver is based on Zhang 's neural-dynamic method and is termed as Zhang neural network (ZNN). The computer simulations performed on a three-link planar robot arm and the PUMA560 manipulator demonstrate the efficacy of the two redundancy-resolution schemes and two RNN QP-solvers presented, as well as the superiority of the ZNN QP-solver compared to the GNN one. More importantly, the simulation results show that the solutions of the two presented schemes fit well with each other, i.e., the two different-level redundancy-resolution schemes could be equivalent in some sense. The theoretical analysis based on the gradient-descent method and Zhang 's neural-dynamic method further substantiates the new finding about the different-level redundancy-resolution equivalence.