Obstacle avoidance of redundant manipulators using neural networks based reinforcement learning

This paper proposes a new approach for solving the problem of obstacle avoidance during manipulation tasks performed by redundant manipulators. The developed solution is based on a double neural network that uses Q-learning reinforcement technique. Q-learning has been applied in robotics for attaining obstacle free navigation or computing path planning problems. Most studies solve inverse kinematics and obstacle avoidance problems using variations of the classical Jacobian matrix approach, or by minimizing redundancy resolution of manipulators operating in known environments. Researchers who tried to use neural networks for solving inverse kinematics often dealt with only one obstacle present in the working field. This paper focuses on calculating inverse kinematics and obstacle avoidance for complex unknown environments, with multiple obstacles in the working field. Q-learning is used together with neural networks in order to plan and execute arm movements at each time instant. The algorithm developed for general redundant kinematic link chains has been tested on the particular case of PowerCube manipulator. Before implementing the solution on the real robot, the simulation was integrated in an immersive virtual environment for better movement analysis and safer testing. The study results show that the proposed approach has a good average speed and a satisfying target reaching success rate.     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

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.     

Geometry-based efficient rata coordination for manipulators with kinematic redundancy

The redundancy resolution problem for kinematically redundant serial chain manipulators is addressed. In this article we present a generalization of the geometry-based rate allocation algorithm, developed initially for only a minimum norm solution, to obtain the optimal joint rate solution for any specified objective function, with or without weightage. This generalization is made possible through a physial interpretation of the common pseudoinverse-based gradient solution scheme, and by developing a modified formulation for the objective function as a minimum criterion not with respect to the origin of the joint rate space, but with respect to another point in the joint rate space represented by the gradient of the specified objective. Application examples of the algorithm including procedures of solution are demonstrated using 7R manipulators with two generic types of geometry. Moreover, a closed form optimal solution for the class of 7R anthropomorphic arms is also given. © 1995 John Wiley & Sons, Inc.     

A balancing technique to stabilize local torque optimization solution of redundant manipulators

A technique that stabilizes the existing local torque optimization solutions for redundant manipulators is proposed in this article. The technique is based on a balancing scheme, which balances a solution of joint torque-minimization against a solution of joint velocity-minimization. Introducing the solution of joint velocity-minimization in the approach prevents occurrence of high joint velocities, and thus results in stable optimal arm motions and guarantees the joint velocities at end of motion to be near zero. Computer simulations were executed on a three-link planar rotary manipulator to verify the performance of the proposed local torque optimization technique and to compare its performance with existing ones for various straight line trajectories. © 1996 John Wiley & Sons, Inc.     

Inverse kinematics of variable-geometry truss manipulators

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry truss manipulators (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. This paper presents a solution to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm has been developed primarily for variable-geometry-truss manipulators, it is general enough for application to other manipulator designs.     

Force polytope and force ellipsoid for redundant manipulators

Evaluation of force/motion capabilities for a manipulator is useful both in the design phase and in the operational phase. Manipulability ellipsoids and polytopes are well-known tools used to represent these capabilities graphically. This article focuses on the evaluation of force capabilities for redundant manipulators, for which additional constraints must be imposed on the available joint torques to satisfy the static assumption. An algorithm to correctly evaluate the task space force polytope is given and a new definition of the force ellipsoid is proposed. The obtained results can be applied also to nonredundant manipulators in singular configurations. Numerical results are provided in the case of a planar redundant arm. ©1997 John Wiley & Sons, Inc.     

Null torque-based dynamic control for kinematically redundant manipulators

For the dynamic control of kinematically redundant manipulators, conventional approaches to local torque minimization have induced physically unachievable joint torques that may exceed the torque limits in the tracing motion of a long end-effector trajectory. This article presents a new control method for redundant manipulators, named the “Null Torque-Based Dynamic Control” (NTDC), which can guarantee stability for joint torques. The proposed method resolves the redundancy at the torque level. The command torque induced by the proposed method is composed of two terms: (1) the minimum-norm torque, which locally minimizes torque loadings at the joints; and (2) the null torque, which is intermittently added to the minimum-norm torque according to a kinematic criterion to globally reduce excessively large torque requirements. In particular, the concept of null torque is based on the property of full row-rank minors for a Jacobian matrix—the aspect that is a function of a manipulator's configuration. The simulation results illustrate that the proposed method is effective for torque optimization when compared with conventional methods.     

A new torque minimization method for heavy-duty redundant manipulators used in nuclear decommissioning tasks

Intelligent Service Robotics - This paper presents an approach to optimize the control torque of heavy-duty redundant manipulators used for dismantling nuclear power plants. Such manipulators must...     

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

A local solution with global characteristics for the joint torque optimization of a redundant manipulator

In this article, a stable local solution with global characteristics is developed for the joint torque optimization problem in redundant robotic manipulators. It is shown that the local optimization of the inertia inverse weighted dynamic torque corresponds to the global kinetic energy minimization problem. The proposed local-global alternative to the joint torque optimization problem is compared for stability and torque optimality with five different methods used for redundancy resolution of robotic manipulators at the acceleration level. The proposed local-global solution has been implemented and tested on a planar four-DOF kinematically redundant lab robot which was designed and built at Southwest Research Institute (SWRI). Several numerical simulations confirm the positive advantages of solutions which have a local as well as a global interpretation. In addition, a “dynamic manipulation index” is introduced to monitor the stability of an optimization problem in a kinematically redundant robot.     

Nonlinear disturbance observer design for robotic manipulators

Robotic manipulators are highly nonlinear and coupled systems that are subject to different types of disturbances such as joint frictions, unknown payloads, varying contact points, and unmodeled dynamics. These disturbances, when unaccounted for, adversely affect the performance of the manipulator. Employing a disturbance observer is a common method to reject such disturbances. In addition to disturbance rejection, disturbance observers can be used in force control applications. Recently, research has been done regarding the design of nonlinear disturbance observers (NLDOs) for robotic manipulators. In spite of good results in terms of disturbance tracking, the previously designed nonlinear disturbance observers can merely be used for planar serial manipulators with revolute joints [Chen, W. H., Ballance, D. J., Gawthorp, P. J., O'Reilly, J. (2000). A nonlinear disturbance observer for robotic manipulators. IEEE Transactions on Industrial Electronics, 47 (August (4)), 932–938; Nikoobin, A., Haghighi, R. (2009). Lyapunov-based nonlinear disturbance observer for serial n-link manipulators. Journal of Intelligent & Robotic Systems, 55 (July (2–3)), 135–153]. In this paper, a general systematic approach is proposed to solve the disturbance observer design problem for robotic manipulators without restrictions on the number of degrees-of-freedom (DOFs), the types of joints, or the manipulator configuration. Moreover, this design method does not need the exact dynamic model of the serial robotic manipulator. This method also unifies the previously proposed linear and nonlinear disturbance observers in a general framework. Simulations are presented for a 4-DOF SCARA manipulator to show the effectiveness of the proposed disturbance observer design method. Experimental results using a PHANToM Omni haptic device further illustrate the effectiveness of the design method.     

分支点邻域内的奇异路径跟踪

在非冗余机械臂运动学的分支奇异点邻域内，由于出现逆运动学解的分支 现象，用基于零空间的拟弧长法求解路径跟踪问题会遇到困难．为此，本文通过计算分支点 的局部模型，提出从分支点开始向两侧延拓的解曲线计算方法，有效地完成了路径跟踪求解 ，在关节空间获得光滑的运动轨迹．     

Inverse statics analysis of planar parallel manipulators via Grassmann-Cayley algebra

The wrench Jacobian matrix plays an important role in the statics and singularity analysis of planar parallel manipulators (PPMs). The Jacobian matrix can be calculated based on the conventional Plücker coordinate method. However, this method cannot be applied when two links are in parallel. A new approach is proposed for the analysis of the forward and inverse wrench Jacobian matrix using Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics analysis is obtained based on the Jacobian. The proposed method can be applied when two links are in parallel. The approach is explained in detail based on a planar 3-RPR PPM example, and the analysis procedure for nine other PPMs is also presented. This novel approach to deriving the statics can be applied to spatial parallel manipulators and redundant cases of PPMs.

     

A Lagrangian network for kinematic control of redundant robotmanipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

Clamping weighted least-norm method for the manipulator kinematic control with constraints

One of the main challenges for kinematic control of manipulators is how to effectively address various constraints, such as obstacle avoidances. Most constraints can be converted into a virtual joint-limit problem by the general weighted least-norm method reported recently. However, a chattering of weighted factors might occur in the presence of disturbances. In this paper, in order to improve the robustness to disturbances, a clamping term forcing joints away from their limits is added to the solution of inverse kinematics, termed as the clamping weighted least-norm method. It is proved that the joint-limit constraint is always guaranteed. The proposed method is applicable to both non-redundant and redundant manipulators; the accuracy of main task is sacrificed only when there is confliction between main task and joint-limit constraint. Experiments on the seven-degree-of-freedom redundant manipulator illustrate the good performance for avoiding joint limits while tracking a given trajectory.