Background

1. Patel et al. [1] map the CRA trajectory into joint space in the redundancy resolution part of AHIC to calculate the JTA trajectory. The task prioritized and singularity robust formulation of redundancy resolution permits the use of extra DOF for fulfilling user defined additional task(s), e.g. See [2–4]. The target acceleration for each additional task is calculated as Equation (1). Shadpey [5] describes the formulation of different additional tasks such as JLA, moving object avoidance, multiple points force control, and posture optimization. In this paper, the JLA task has been implemented (see [5] for a detail description). In the AHIC scheme, redundancy resolution is implemented at the acceleration level. The damped least-squares solution is given by Equation (2). Where (3 × 7) and (3 × 7) are the Jacobean matrices projecting the joint rates to linear and angular velocities of the frame {T}, , and ω, respectively. The matrices (3 × 3), (3 ×3), and (3 × 3) are diagonal weighting matrices to assign priority to position/force tracking, orientation/torque tracking, and the singularity avoidance tasks. Yaghoob Azizi1, Nima Azhdar zadeh2 Background Redundancy resolution References [1] Rajni V. Patel, Fellow, IEEE, Heidar A. Talebi, Senior Member, IEEE, JagadeesanJayender, Member, IEEE, and FarshidShadpey, “A Robust Position and Force Control Strategy for 7-DOF Redundant Manipulators”, IEEE/ASME Transactions on Mechatronics.14 (2009)No5. [2] H. Seraji, Configuration control of redundant manipulators: Theory and implementation, IEEE Trans. Robot. Autom, 5 (1989) No. 4 472–490. [3] H. Seraji and R. Colbaugh, Singularity-robustness and task prioritization in configuration control of redundant robots, in Proc. 29th IEEE Conf. Decision Control, (1990) 3089–3095. [4] F. Shadpey, R. V. Patel, C. Balafoutis, and C. Tessier, Compliant motion control and redundancy resolution for kinematically redundant manipulators, Proc. Amer. Control Conf.,(1995) 392–396. [5] F. Shadpey, R. V. Patel, C. Balafoutis, and C. Tessier, Compliant motion control and redundancy resolution for kinematically redundant manipulators, Proc. Amer. Control Conf., (1995) 392–396. The authors would like to thank Dr. Heidar A. Talebi of Amirkabir University of technology with regard to his assistance in PA10 manipulator. 1Department of Electrical Engineering, Amirkabir University of Technology, 2Department of Electrical Engineering, Sahand University of Technology Experimental results and analysis Acknowledgements In this part the control signal maps from Cartesian space to joint space and a signal can be added to the control signal to modify shortages or increase the robot capability to do special tasks. For example the control signal may be charged in this part so that takes the robot away from singular configurations. A signal named ALPHAZ is defined as noted in Code 1. ALPHAZ is added to the control signal, obtained in redundancy resolution. Code 1: Land=150; b=[1;1;1;1;1;1;1]; Iden=eye(7); JP=J'/(J*J'); Alphaz = (Iden-JP*J)*b; Alphaz = Alphaz*Land; - Signal X versus its reference signal for LANDA1=1 and LANDA2=0.2 Discussion In this paper singularity avoidance is implemented at acceleration level, the proposed algorithm is aimed at increasing robots runtime using a modified control signal. In this paper the computer program simulates and controls PA10 robot in two ways. In this procedure a trajectory of 5 Degree of freedom is defined based on inputs position, velocity and acceleration. Results showed that the proposed algorithm increases the robots runtime up to 3 times greater than that of achieved by Patel. Several type of control functions were examined for improving redundancy resolution capability of generating control signals close enough to expected ones and that bypass the singular configurations. An optimization was performed on all the methods used. This type of modified redundancy resolution strategy could be used for similar redundant robotic arms. Conclusion Results showed that the proposed algorithm increases the robots runtime up to 3 times greater than that of achieved by Patel. Smoother motion profile can be achieved for redundant robots using the proposed method. An improved redundancy resolution based on the proposed method led to improvement in singularity avoidance and a strategy is developed to investigate robots singularity avoidance capability relative to the Patel’s work. Patel used a control signal with the focus on the extra task and the proposed algorithm promoted the Patel’s control signal and increased its singularity avoidance capability. Results showed that modifying control signal using redundancy resolution can increase the singularity avoidance in 7-DOF PA10 robotic arm. Defining a sliding mode control function for redundant robots in the redundancy resolution part gave the robot the ability to most properly handle the singular configurations. - Robot Runtime with parameter LAND variable compared with that of Patel’s work. A Modified Control Approach to Increase Singularity Avoidance in 7-DOF Redundant Arms (1) (2) (3) (4) The subscript c refers to additional task. However, the redundancy resolution scheme employed in this paper is based on task augmentation and therefore if the number of specified secondary tasks corresponds to a non-singular square augmented Jacobean, the damped least-square has a unique solution. Moreover, since singularity avoidance was considered as an additional task, the square Jacobean never reached a singular configuration. Hence, the notion of dynamic inconsistency does not arise here, since the null space of the Jacobean is in fact empty. Moreover, a velocity feedback term λ is introduced in redundancy resolution to prevent instability. A proper value of λ can ensure the stability of the solution. To verify the performance of the modified redundancy resolution scheme presented by Patel et al. [1], a simulation was performed. Considering the worst-case performance, the final position/orientation was selected such that makes the robots posture approach a singular configuration. This induces a high null-space component on the joint velocities. In this paper this part of the problem is being solved by having robot away from singular configurations by updating control signal. Simulations showed that by the use of proposed strategy, the position/force control algorithm by Patel et al [1] invigorates and makes its singularity avoidance better. Equation (5) shows the formula which is used in the redundancy resolution. In Equation (5) matrices and are as indicated in Equation (6) and Equation (7). =Landa1*eye(3) (6) =Landa2*eye(7) (7) Matrix is actually a weighting matrix for position/force trajectory and parameter LANDA1 plays an important role in tuning the weighting matrix . Matrix is a weighting matrix for singularity avoidance and parameter LANDA2 plays an important role in tuning the weighting matrix . In the best result robot had an acceptable performance in position tracking and also worked well in force control. (5)