Joint-acceleration Level Research Articles

Smoothness-oriented path optimization for robotic milling processes

Industrial robots are increasingly used for five-axis machining operations, where the rotation of the end effector along the tool-axis direction is functionally redundant. This functional redundancy should be carefully resolved when planning the robot path according to the tool path generated by a computer-aided manufacturing (CAM) system. Improper planning of the redundancy may cause drastic variations of the joint motions, which could significantly decrease the machining efficiency as well as the machining accuracy. To tackle this problem, this paper presents a new optimization-based methodology to globally resolve the functional redundancy for the robotic milling process. Firstly, a global performance index concerning the smoothness of the robot path at the joint acceleration level is proposed. By minimizing the smoothness performance index while considering the avoidance of joint limits and the singularity and the constraint of the stiffness performance, the resolution of the redundancy is formulated as a constrained optimization problem. To efficiently solve the problem, the sequential linearization programming method is employed to improve the initial solution provided by the conventional graph-based method. Then, simulations for a given tool path are presented. Compared with the graph-based method, the proposed method can generate a smoother robot path in which a significant reduction of the magnitude of the maximum joint acceleration is obtained, resulting in a smoother tool-tip feedrate profile. Finally, the experiment on the robotic milling system is also presented. The results show that the optimized robot path of the proposed method obtains better surface quality and higher machining efficiency, which verifies the effectiveness of the proposed method.

Acceleration-Level Configuration Adjustment Scheme for Robot Manipulators

In this article, configuration adjustment (CA) for robot manipulators at the joint-acceleration level is presented. Specifically, a new acceleration-level performance index for achieving CA is designed by employing the neurodynamic method. Thus, based on this performance index, and by incorporating joint physical constraints (i.e., joint-configuration, -velocity, and -acceleration limits), a novel acceleration-level CA (ALCA) scheme for robot manipulators is proposed and investigated. The proposed ALCA scheme is transformed into a quadratic program and calculated using a neural network solver. Comparative simulation results obtained with a four-link robot manipulator are presented to substantiate the effectiveness and superiority of the proposed ALCA scheme compared with those of the velocity-level CA scheme. Moreover, simulations and experiments are conducted on a practical Epson robot manipulator to demonstrate the physical realization of the proposed ALCA scheme.

Bi-criteria minimization with MWVN–INAM type for motion planning and control of redundant robot manipulators

SUMMARYThis study proposes and investigates a new type of bi-criteria minimization (BCM) for the motion planning and control of redundant robot manipulators to address the discontinuity problem in the infinity-norm acceleration minimization (INAM) scheme and to guarantee the final joint velocity of motion to be approximate to zero. This new type is based on the combination of minimum weighted velocity norm (MWVN) and INAM criteria, and thus is called the MWVN–INAM–BCM scheme. In formulating such a scheme, joint-angle, joint-velocity, and joint-acceleration limits are incorporated. The proposed MWVN–INAM–BCM scheme is reformulated as a quadratic programming problem solved at the joint-acceleration level. Simulation results based on the PUMA560 robot manipulator validate the efficacy and applicability of the proposed MWVN–INAM–BCM scheme in robotic redundancy resolution. In addition, the physical realizability of the proposed scheme is verified in practical application based on a six-link planar robot manipulator.

Acceleration-Level Inequality-Based MAN Scheme for Obstacle Avoidance of Redundant Robot Manipulators

In this paper, a new inequality-based criterion is proposed and investigated for obstacle avoidance of redundant robot manipulators at the joint-acceleration level. By incorporating such a dynamically updated inequality criterion and the joint physical constraints (i.e., joint-angle limits, joint-velocity limits, and joint-acceleration limits), a novel minimum-acceleration-norm (MAN) scheme is presented and investigated for robots' redundancy resolution. In addition, the resultant obstacle-avoidance MAN scheme resolved at the joint-acceleration level is reformulated as a general quadratic program (QP). Moreover, two important “Bridge” theorems are established, which show that such a QP problem can be equivalent to linear variational inequality (LVI) and then to piecewise-linear projection equation (PLPE). An LVI-based numerical method is thus developed and applied for online solution of the QP problem and the inequality-based obstacle-avoidance MAN scheme. Simulative results based on the PA10 robot manipulator in the presence of window-shaped and point obstacles further demonstrate the efficacy and superiority of the proposed acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators. In addition, experimental verification conducted on a practical six-link planar robot manipulator substantiates the effectiveness and physical realizability of the proposed obstacle-avoidance scheme.

Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators

SUMMARYIn this paper, a pseudoinverse-type bi-criteria minimization scheme is proposed and investigated for the redundancy resolution of robot manipulators at the joint-acceleration level. Such a bi-criteria minimization scheme combines the weighted minimum acceleration norm solution and the minimum velocity norm solution via a weighting factor. The resultant bi-criteria minimization scheme, formulated as the pseudoinverse-type solution, not only avoids the high joint-velocity and joint-acceleration phenomena but also causes the joint velocity to be near zero at the end of motion. Computer simulation results based on a 4-Degree-of-Freedom planar robot manipulator comprising revolute joints further verify the efficacy and flexibility of the proposed bi-criteria minimization scheme on robotic redundancy resolution.

G2-type SRMPC scheme for synchronous manipulation of two redundant robot arms.

In this paper, to remedy the joint-angle drift phenomenon for manipulation of two redundant robot arms, a novel scheme for simultaneous repetitive motion planning and control (SRMPC) at the joint-acceleration level is proposed, which consists of two subschemes. To do so, the performance index of each SRMPC subscheme is derived and designed by employing the gradient dynamics twice, of which a convergence theorem and its proof are presented. In addition, for improving the accuracy of the motion planning and control, position error, and velocity, error feedbacks are incorporated into the forward kinematics equation and analyzed via Zhang neural-dynamics method. Then the two subschemes are simultaneously reformulated as two quadratic programs (QPs), which are finally unified into one QP problem. Furthermore, a piecewise-linear projection equation-based neural network (PLPENN) is used to solve the unified QP problem, which can handle the strictly convex QP problem in an inverse-free manner. More importantly, via such a unified QP formulation and the corresponding PLPENN solver, the synchronism of two redundant robot arms is guaranteed. Finally, two given tasks are fulfilled by 2 three-link and 2 five-link planar robot arms, respectively. Computer-simulation results validate the efficacy and accuracy of the SRMPC scheme and the corresponding PLPENN solver for synchronous manipulation of two redundant robot arms.

Simultaneous repetitive motion planning of two redundant robot arms for acceleration-level cooperative manipulation

This Letter proposes a novel simultaneous repetitive motion planning (SRMP) scheme of two redundant robot arms for cooperative manipulation. To remedy the joint-angle drift phenomenon, two SRMP subschemes are exploited at the joint-acceleration level. The subschemes are then simultaneously reformulated as two quadratic programs (QPs), which are finally unified into a QP problem solving. Theoretical analysis and computer simulation based on two three-link robot arms both substantiate the feasibility and effectiveness of the proposed SRMP scheme. • A two-manipulator robotic system is investigated. • A novel simultaneous repetitive motion planning scheme is proposed. • Theoretical analysis of GD-ZD type is presented. • A unified quadratic program is achieved. • Computer simulation substantiates the effectiveness of the proposed scheme.

Acceleration-Level Repetitive Motion Planning and Its Experimental Verification on a Six-Link Planar Robot Manipulator

To solve nonrepetitive problems, this brief proposes and investigates a novel repetitive motion planning (RMP) scheme (termed acceleration-level RMP scheme), which is resolved at the joint-acceleration level rather than at the joint-velocity level. The scheme is then reformulated as a quadratic program (QP) subject to equality and bound constraints. For the purposes of experimentation, a discrete-time QP solver is developed for the solution of the resultant QP. In addition, the global convergence of such a discrete-time QP solver is presented and analyzed. Comparisons between the nonrepetitive motion and repetitive motion planning validate the effectiveness and superiority of the proposed scheme. More importantly, the proposed scheme and the corresponding discrete-time QP solver are implemented on a six-link planar robot manipulator. The experimental results further substantiate their physical realizability, efficiency, and accuracy.

Different-Level Simultaneous Minimization of Joint-Velocity and Joint-Torque for Redundant Robot Manipulators

In J Robot Syst 13(3):177---185 (1996), Ma proposed an efficient technique to stabilize local torque optimization solution of redundant manipulators, which prevents occurrence of high joint-velocity and guarantees the final joint-velocity to be near zero. To prevent the same problems, a different-level simultaneous minimization scheme is proposed in this paper for robotic redundancy resolution, which combines the minimum two-norm joint-velocity and joint-torque solutions via two weighting factors. Physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are also taken into consideration in such a scheme-formulation. Moreover, the proposed different-level simultaneous minimization scheme is resolved at the joint-acceleration level and reformulated as a general quadratic program (QP). Computer-simulation results based on the PUMA560 robot manipulator performing different types of end-effector path-tracking tasks demonstrate the validity and advantage of the proposed different-level simultaneous minimization scheme. Furthermore, experimental verification conducted on a practical six-link planar robot manipulator substantiates the effectiveness and the physical realizability of the proposed scheme.

Acceleration-level repetitive motion planning of redundant planar robots solved by a simplified LVI-based primal-dual neural network

In this paper, we propose a novel repetitive motion planning (RMP) scheme at the joint-acceleration level (termed, the acceleration-level RMP scheme, the ARMP scheme), which incorporates joint-angle limits, joint-velocity limits and joint-acceleration limits. To do this, Zhang et al's neural-dynamic method is employed to derive and design such an ARMP scheme. Such a scheme is then reformulated as a quadratic program (QP). To solve this QP problem online, a simplified linear-variational-inequality based primal-dual neural network (i.e., S-LVI-PDNN) is designed. With simple piecewise-linear dynamics and global exponential convergence to the optimal solution, such an S-LVI-PDNN solver can handle the strictly convex QP problem in an inverse-free manner. Finally, three given tasks, i.e., rhombic path, straight-line path and square path tracking tasks, are fulfilled by three-link, four-link and five-link planar robot arms, respectively. Computer-simulation and physical experiment results validate the physical realizability, efficacy and accuracy of the ARMP scheme and the corresponding S-LVI-PDNN solver.

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.

Acceleration-Level Cyclic-Motion Generation of Constrained Redundant Robots Tracking Different Paths

In this paper, a cyclic-motion generation (CMG) scheme at the acceleration level is proposed to remedy the joint-angle drift phenomenon of redundant robot manipulators which are controlled at the joint-acceleration level or torque level. To achieve this, a cyclic-motion criterion at the joint-acceleration level is exploited. This criterion, together with the joint-angle limits, joint-velocity limits, and joint-acceleration limits, is considered into the scheme formulation. In addition, the neural-dynamic method of Zhang is employed to explain and analyze the effectiveness of the proposed criterion. Then, the scheme is reformulated as a quadratic program, which is solved by a primal-dual neural network. Furthermore, four tracking path simulations verify the effectiveness and accuracy of the proposed acceleration-level CMG scheme. Moreover, the comparisons between the proposed acceleration-level CMG scheme and the velocity-level scheme demonstrate that the former is safer and more applicable. The experiment on a physical robot system further verifies the physical realizability of the proposed acceleration-level CMG scheme.

Different-level two-norm and infinity-norm minimization to remedy joint-torque instability/divergence for redundant robot manipulators

To remedy the joint-torque instability/divergence phenomenon arising in the conventional infinity-norm torque-minimization (INTM) scheme, and prevent the occurrence of high joint-velocity and joint-acceleration as well, a different-level bi-criteria minimization scheme is proposed and investigated in this paper for redundant robot manipulators with physical constraints (e.g., joint-angle limits, joint-velocity limits and joint-acceleration limits) considered. Such a scheme combines the minimum two-norm joint-velocity and infinity-norm joint-torque solutions via a weighting factor, which guarantees the final joint-velocity of the motion to be near zero (more acceptable for engineering application). In addition, the different-level scheme is reformulated as a general quadratic program (QP) and resolved at the joint-acceleration level. Computer-simulation results based on the PUMA560 robot manipulator further demonstrate the effectiveness and advantages of the proposed different-level bi-criteria minimization scheme for robotic redundancy resolution.

Two/Infinity Norm Criteria Resolution of Manipulator Redundancy at Joint-Acceleration Level Using Primal-Dual Neural Network

A two/infinity norm criteria (termed bi-criteria) weighting scheme is proposed in this paper for resolving manipulator redundancy at the joint-acceleration level. This bi-criteria scheme is aimed at remedying discontinuity-points and torque-instability problems which arise in pure infinity-norm acceleration-minimization schemes. By incorporating joint physical limits, the proposed bi-criteria redundancy-resolution scheme can finally be formulated as a quadratic program (QP) subject to equality constraint, inequality constraint and bound constraint simultaneously. As a real-time QP solver with simple piecewise-linear dynamics and higher computational efficiency, the primal-dual neural network based on linear variational inequalities (LVI) is presented in this paper to solve online such a bi-criteria weighting scheme. Computer-simulation results based on a PMUA560 robot arm illustrate the advantages and efficacy of such a neural weighting scheme.

Emerging motor behaviors: Learning joint coordination in articulated mobile robots

In this paper, we analyze the insights behind the common approach to the assessment of robot motor behaviors in articulated mobile structures with compromised dynamic balance. We present a new approach to this problem and a methodology that implements it for motor behaviors encapsulated in rest-to-rest motions. As well as common methods, we assume the availability of kinematic information about the solution to the task, but reference is not made to the workspace, allowing the workspace to be free of restrictions. Our control framework, based on local control policies at the joint acceleration level, attracts actuated degrees of freedom (DOFs) to the desired final configuration; meanwhile, the resulting final states of the unactuated DOFs are viewed as an indirect consequence of the profile of the policies. Dynamical systems are used as acceleration policies, providing the actuated system with convenient attractor properties. The control policies, parameterized around imposed simple primitives, are deformed by means of changes in the parameters. This modulation is optimized, by means of a stochastic algorithm, in order to control the unactuated DOFs and thus carry out the desired motor behavior.

Obstacle avoidance control for redundant manipulators using collidability measure

We present an efficient obstacle avoidance control algorithm for redundant manipulators using a new measure called collidability measure. Considering moving directions of manipulator links, the collidability measure is defined as the sum of inverse of predicted collision distances between links and obstacles: This measure is suitable for obstacle avoidance since directions of moving links are as important as distances to obstacles. For kinematic or dynamic redundancy resolution, null space control is utilized to avoid obstacles by minimizing the collidability measure: We present a velocity-bounded kinematic control law which allows reasonably large gains to improve the system performance. Also, by clarifying decomposition in the joint acceleration level, we present a simple dynamic control law with bounded joint torques which guarantees tracking of a given end-effector trajectory and improves a kinematic cost function such as collidability measure. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.

Dynamic redundancy resolution of redundant manipulators with local optimization of a kinematic criterion

To consider the dynamic effects of redundancy resolution in redundant manipulators, the inverse kinematics of the redundant manipulator must be resolved at the acceleration level, focussing mainly on using selective dynamic criteria to resolve the redundancy. These local dynamic redundancy resolution techniques reveal some instability problems due to the high joint velocities. The buildup of high joint velocities is due to the lack of a kinematic criterion in the local optimization process to reflect the changes of joint velocities. In order to avoid instability due to high joint velocities, this paper proposes dynamic redundancy resolution techniques (SMV and SMTV) which locally optimize the performance function, including a kinematic criterion as the norm of joint velocities to reflect the changes of joint velocities. These prevent the occurrence of high joint velocities and guarantee that joint velocities at end of motion are near zero. In addition, the redundancy is resolved at the joint acceleration level to consider the manipulator dynamics and the effect of kinematic criterion on the manipulator joint torques. Computer simulations were performed on a three-link planar rotary manipulator to verify the performance of the proposed dynamic redundancy resolution techniques and to compare its performance with existing local dynamic redundancy resolution techniques.

A unified approach to the inverse kinematic solution for a redundant manipulator

SUMMARYFor a kinematically redundant manipulator, some performance indices can be optimized while carrying out a given task. So far, the redundancy resolution has been solved at the joint angle level, the joint velocity level, or joint acceleration level depending on the performance indices. According to the resolution level, the solution is represented by high-order differential equations or superfluous number of equations. We propose a unified approach to the inverse kinematic solution which optimizes it at the joint velocity level regardless of the types of the performance indices. A unified approach to obtain an optimal joint velocity is derived by using the necessary condition for optimality so that the proposed method provides an optimal solution for any performance indices and tasks. The optimal solution becomes a set of the minimum number of first-order differential equations which requires a minimum search dimension.To show the validity of the approach, it is applied to a three-link planar manipulator for various types of performance indices.