PUMA Manipulator Research Articles

Inverse kinematic solution and singularity avoidance using a deep deterministic policy gradient approach

<p>The robotic arm emerges as a subject of paramount significance within the industrial landscape, particularly in addressing the complexities of its kinematics. A significant research challenge lies in resolving the inverse kinematics of multiple degree of freedom (M-DOF) robotic arms. The inverse kinematics of M-DOF robotic arms pose a challenging problem to resolve, thus it involves consideration of singularities which affect the arm robot movement. This study aims a novel approach utilizing deep reinforcement learning (DRL) to tackle the inverse kinematic problem of the 6-DOF PUMA manipulator as a representative case within the M-DOF manipulator. The research employs Jacobian matrix for the kinematics system that can solve the singularity, and deep deterministic policy gradient (DDPG) as the kinematics solver. This chosen technique offers enhancing speed and ensuring stability. The results of inverse kinematic solution using DDPG were experimentally validated on a 6-DOF PUMA arm robot. The DDPG successfully solves inverse kinematic solution and avoids the singularity with 1,000 episodes and yielding a commendable total reward of 1,018.</p>

Adaptive Visual Control for Robotic Manipulators with Consideration of Rigid-Body Dynamics and Joint-Motor Dynamics

A novel cascade visual control scheme is proposed to tailor for electrically driven robotic manipulators that operate under kinematic and dynamic uncertainties, utilizing an uncalibrated stationary camera. The proposed control approach incorporates adaptive weight radial basis function neural networks (RBFNNs) to learn the behaviors of the uncertain dynamics of the robot and the joint actuators. The controllers are designed to nullify the approximation error and mitigate unknown disturbances through an integrated robust adaptive mechanism. A major advantage of the proposed approach is that prior knowledge of the dynamics of the robotic manipulator and its actuator is no longer required. The controller autonomously assimilates the robot and actuator dynamics online, thereby obviating the need for fussy regression matrix derivation and advance dynamic measurement to establish the adaptive dynamic parameter update algorithm. The proposed scheme ensures closed-loop system stability, bounded system states, and the convergence of tracking errors to zero. Simulation results, employing a PUMA manipulator as a testbed, substantiate the viability of the proposed control policy.

Uncalibrated Adaptive Visual Servoing of Robotic Manipulators with Uncertainties in Kinematics and Dynamics

In the study, we propose a novel adaptive visual servoing control scheme for robotic manipulators with kinematic and dynamic uncertainties, where the camera used is uncalibrated, which implies that its intrinsic and extrinsic parameters are unavailable for measurement. For our scheme, a depth-independent composite Jacobian matrix is constructed to make visual parameters and robotic physical parameters appear linearly in a parametrized uniform form so that an adaptive algorithm can be developed to estimate their values. With the raised adaptive algorithm, the potential singularity of the Jacobian matrix can be well circumvented by updating estimated parameters in an appropriate tiny range of actual values. With our scheme, the asymptotic convergence of the image tracking error to zero is established successfully, in addition to the signal boundedness of the closed-loop system. The effectiveness of the proposed scheme is confirmed by simulation results based on a 6-DOF PUMA manipulator.

Automatic selection of the Groebner Basis’ monomial order employed for the synthesis of the inverse kinematic model of non-redundant open-chain robotic systems

The methods most commonly used to synthesize the Inverse Kinematic Model (IKM) of open-chain robotic systems strongly depend on the robot’s geometry, which make them difficult to systematize. In a previous work we presented a systematic procedure that relies on Groebner Bases to synthesize the IKM of non-redundant open-chain robots. This study expands the developed procedure with a methodology for the automatic selection of the basis’ monomial order. The procedure’s inputs are the robot’s Denavit-Hartenberg parameters and the movement range of its actuators, while the output is the synthesized IKM, ready to be used in the robot’s control system or in a simulation of its behavior. This procedure can synthesize the IKM of a wide range of open-chain robotic systems, such as Cartesian robots, SCARA, non-redundant multi-legged robots, and all non-redundant manipulators that satisfy the in-line wrist condition. The procedure’s performance is assessed through two study cases of open-chain robots: a walking hexapod and a PUMA manipulator. The optimal monomial order is successfully identified for all cases. Also the output errors of the synthesized IKMs are negligible when evaluated in their corresponding workspaces, while their computation times are comparable to those required by the kinematic models calculated by traditional methods.

Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

One of the most important elements of a robot’s control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot’s actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot’s structure. The inputs to the developed procedure are the robot’s Denavit–Hartenberg parameters, while the output is the IKM, ready to be used in the robot’s control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugère’s F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure’s performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.

Trajectory Optimization of Robots With Regenerative Drive Systems: Numerical and Experimental Results

In this paper, we investigate energy-optimal control of robots with ultracapacitor-based regenerative drive systems. Based on a previously introduced framework, a fairly generic model is considered for the robot and the drive system. An optimal control problem is formulated to find point-to point trajectories maximizing the amount of energy regenerated and stored in the capacitor. The optimization problem, its numerical solution, and an experimental evaluation are demonstrated using a PUMA manipulator with custom regenerative drives. Power flows, stored regenerative energy, and efficiency are evaluated. Tracking of optimal trajectories is enforced on the robot using a standard robust passivity based control approach. Experimental results show that when following optimal trajectories, a reduction of about $\text{10}\text{--}\text{22}\%$ in energy consumption can be achieved for the conditions of the study, relative to the nonregenerative case.

Generalized solution for inverse kinematics problem of a robot using hybrid genetic algorithms

The robot control consists of kinematic control and dynamic control. Control methods of the robot involve forward kinematics and inverse kinematics (IK). In Inverse kinematics the joint angles are found for a given position and orientation of the end effector. Inverse kinematics is a nonlinear problem and has multiple solutions. This computation is required to control the robot arms. A Genetic Algorithm (GA) and Hybrid genetic algorithm (HGA) (Genetic Algorithm in conjunction with Nelder-Mead technique) are proposed for solving the inverse kinematics of a robotic arm. HGA introduces two concepts exploration, exploitation. In an exploration phase, the GA identifies the good areas in entire search space and then exploitation phase is performed inside these areas by using Nelder- mead technique Binary Simulated Crossover and niching strategy for binary tournament selection operator is used. Proposed algorithms can be used on any type of manipulator and the only requirement is the forward kinematic equations, which are easily obtained. As a case study inverse kinematics of a Two Link Elbow Manipulator and PUMA manipulator are solved using GA and HGA in MATLAB. The algorithm is able to find all solutions without any error

Comparison of Techniques for Disturbance-Tolerant Position Control of the Manipulator of PUMA Robot using PID

Objectives: The control of the robotic manipulator arm under a variety of faults has been studied and the performance is compared using PID and other technique. Methods/Statistical Analysis: In a highly nonlinear environment such as manipulator of a robot, employing more than one control techniques yields desirable results. Here, a combination of PID along with pole-placement control of linear model has been designed. The feedback control gains have been obtained offline using equivalent linearization of the nonlinear coupled robot dynamic system. The input torque has been obtained from PID. The combined torque has been applied to the joints. This scheme has been implemented online in a standard PUMA manipulator with the payload. Findings: It has been observed that PID as compared to modified pole placement method is more efficient to control a robotic arm. Application/Improvement: The proposed hybrid control approach involving offline designs and their online implementation on six degrees of freedom robot has been found to be efficient and capable of accommodating common types of faults represented as an exponential or sine or a constant function but sudden or abrupt in nature.

Maximum load of flexible joint manipulators using nonlinear controllers

SUMMARYThe main innovation of this paper is determining the dynamic load carrying capacity (DLCC) of a flexible joint manipulator (FJM) using a closed form nonlinear optimal control approach. The proposed method is compared with two closed loop nonlinear methods that are usually applied to robotic systems. As a new idea, DLCC of the manipulator is considered as a criterion to compare how well controllers perform point to point mission for the FJMs. The proposed method is compared with feedback linearization (FL) and robust sliding mode control (SMC) methods to show better performance of proposed nonlinear optimal control approach. An optimal controller is designed by solving a nonlinear partial differential equation named the Hamilton–Jacobi–Bellman (HJB) equation. This equation is complicated to solve exactly for complex dynamics so it is solved numerically using an iterative approximation combined with the Galerkin method. In the FL method, angular position, velocity, acceleration and jerk of links are considered as new states to linearize the dynamic equations. In the case of SMC, the dynamic equations of manipulator are changed to the standard form then the Slotine method is used to design the sliding mode controller. Two simulations are performed for a planar and a spatial Puma manipulator and performances of controllers are compared. Finally an experimental test is done on 6R manipulator and the Stereo vision method is used to determine the position and orientation of the end-effector.

Nonlinear Identification of a PUMA Manipulator Arm MA2000

This article deals with the tuning of a simplified non-linear model that represents the dynamic behavior of the manipulator arm PUMA MA2000, where excitation signals formed by a finite sum of harmonics Fourier series were used in order to obtain arm dynamical responses. Initially, non-linear mathematical model is derived by using the Euler-Lagrange notation, and then a simplified nonlinear model is obtained and tuned by using the experimental angular position measurements for waist, shoulder and elbow robot joints.

A calibration method for enhancing robot accuracy through integration of an extended Kalman filter algorithm and an artificial neural network

Robot position accuracy plays an important role in advanced industrial applications. In this paper, a new calibration method for enhancing robot position accuracy is proposed. In order to improve robot accuracy, the method first models and identifies its geometric parameters using an extended Kalman filtering (EKF) algorithm. Because the non-geometric error sources (such as the link deflection errors, joint compliance errors, gear backlash, and so on) are either difficult or impossible to model correctly and completely, an artificial neural network (ANN) will be applied to compensate for these un-modeled errors. The combination of model-based identification of the robot geometric errors using EKF and a compensation technique using the ANN could be an effective solution for the correction of all robot error sources. In order to demonstrate the effectiveness and correctness of the proposed method, simulated and experimental studies are carried out on serial PUMA and HH800 manipulators, respectively. The enhanced position accuracy of the robots after calibration confirms the practical effectiveness and correctness of the method.

Determination of joint reaction forces in a symbolic form in rigid multibody systems

This paper presents an algorithm for determination of joint reaction forces in a symbolic form in planar and spatial tree structure rigid multibody systems . The frictionless revolute and prismatic joints are taken into consideration. The algorithm is based on the use of Kane's equations with undetermined multipliers of constraints. The expressions for the reaction forces and the torques of reaction couples in the joints are obtained in a form that does not require matrix inversion and allows an easy and straightforward implementation in programming environments for symbolic computations (like Mathematica, Maple etc.). The application of the proposed algorithm to the problem of determination of static friction forces in locked Coulomb friction joints is indicated. The algorithm has been illustrated by using both a gymnast on a trampoline and a Puma manipulator. ► The frictionless revolute and prismatic joints are considered. ► Joint reactions in tree structure multibody systems are determined in a symbolic form. ► Kane's equations with undetermined multipliers of constraints are used. ► Theoretical results are illustrated through 2 examples.

Singular planes of serial wrist-partitioned manipulators and their singularity metrics

Current metrics measuring proximity to kinematic singularities are based on mathematical characteristics of the Jacobian matrix such as manipulability or the conditioning index. This paper develops a geometric representation of the kinematic singularities of wrist-partitioned manipulators in terms of singular planes. It is shown that the determinant of the Jacobian matrix is a product of the distances from the controlled points on the end-effector to these singular planes. The paper proposes that for wrist-partitioned manipulators these distances can be used as singularity metrics which directly measure proximity to kinematic singularities. The Puma manipulator is used as an example.

Robot positioning of flexible-link manipulator using vision

Vision-aided flexible link robot positoning using the Camera Space Manipulation (CSM) method is developed. The primary motivation for this work is to use an autonomous vision-aided robotic system to pick-up and accurately move a flexible object that it encounters. The work consists of analytical and experimental investigation of the performance of CSM for a kinematic model of the PUMA manipulator with a flexible structure at the wrist which accounts for the gravitation. Trade-offs between camera view parameters and axial deflection model parameters were investigated. View parameter reestimation and maneuvering resulted a very accurate placement of the end-effector at the target.

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.

Modified Jacobian method of transversal passing through the smallest deficiency singularities for robot manipulators

This paper proposes a method for transversal passing through singularities of corank 1, both for nonredundant and redundant robotic manipulators. The method modifies the Jacobian matrix of manipulator's forward kinematics to retrieve its full rank at singularities. Natural candidates for the Jacobian matrix modification are derivatives of determinants of full size sub-matrices of the Jacobian matrix. The method is illustrated with examples, including a PUMA manipulator and 2-link and 3-link planar manipulators. Some restrictions on the applicability of the method for nonredundant manipulators are also discussed.

1320 6-DOF マニピュレータによるリハビリテーション支援に関する研究

We think about kinesitherapy movement as rehabilitation which a physical therapist takes, and have developed the programs for a robot manipulator which lets handicapped persons to do such exercise assisting a physical therapist. And, we evaluated the programs. In this study, we propose a method using a manipulator, and we confirm the practicability for the arm-kinesitherapy movements. In the experiment, we used a 6-DOF PUMA manipulator which assists of a physical therapist. As a role of a patient, we used a 2-DOF manipulator for measuring the distribution of load from the 6-DOF PUMA manipulator. We can measure angles of the joints, the torque which the patient manipulator gives the physical therapist manipulator from torque sensors and the stress on the forearm part of a patient manipulator from distortion gauge. We compared the real torque of a patient manipulator with the calculated torque of it from the sensors on the physical therapist manipulator such as rotation velocity and torque at each joint.

A Workcell for the Development of Robot-Assisted Surgical Procedures

This paper describes a robotic workstation for the development of new robot-assisted surgical procedures. This work is motivated by the difficulties and cost associated to the development of surgical robots, often requiring large investments and several re-designs which limit wider use of this technology. The approach presented here consists of using a general purpose robotic workcell to develop the hardware and the surgical aspects of new robot-based surgical systems, before committing to a completely new system design. The workcell is based on a clean room PUMA 260 manipulator, suitably enhanced to expand and improve its capabilities, and on a vision-based operator interface. Two new robot-assisted surgical procedures have been developed and tested using this set-up: percutaneous discectomy and knee osteoctomy. By using the robotic workcell, engineers and surgeons are able to define many aspects of the two procedures, such as surgical gestures, workspace of the robot, and calibration procedures, without incurring a large, up-front investment. First, the article describes the configuration of the workcell, the enhancements to the PUMA manipulator and the surgical procedures developed with this setup. Then the results of the tests and the lessons learned using the workcell are discussed in some detail.

Disturbance rejection for space-based manipulators

This paper describes the implementation of a disturbance rejection controller for a 6-DOF PUMA manipulator mounted on a 3-DOF platform. A control algorithm is designed to track the desired position and attitude of the end-effector in inertial space, subject to unknown disturbances in the platform axes. Experimental results are presented for step, sinusoidal, and random disturbances in the platform rotational axis and in the neighborhood of kinematic singularities. >

On the use of linear camera-object interaction models in visual servoing

We investigate the exploitation of linear models of camera-object interaction for an efficient modeling and control of image-based visual servoing systems. The approach includes a method for coping with those representation ambiguities typical of linear interaction models which may affect both planning and control. The implementation of an eye-in-hand servoing system based on affine camera models and using image contours as relevant visual features is described and discussed. The system, including an image planner, a two-dimensional/three-dimensional (2-D/3-D) controller, and a visual analysis module, allows an intuitive specification and execution of relative positioning tasks w.r.t. still or moving rigid objects. Results of real-time experiments with a robotic platform featuring a PUMA manipulator provide a further insight into characteristics and performance of affine visual servoing systems.