Abstract

This paper presents a method that can reduce the computational cost of the hierarchical quadratic programming (HQP)-based robot controller. Hierarchical controllers can effectively manage articulated robots with many degrees of freedom (DoFs) to perform multiple tasks. The HQP-based controller is one of the generic hierarchical controllers that can provide a control solution guaranteeing strict task priority while handling numerous equality and inequality constraints. However, according to a large amount of computation, it can be a burden to use it for real-time control. Therefore, for practical use of the HQP, we propose a method to reduce the computational cost by decreasing the size of the decision variable. The computation time and control performance of the proposed method are evaluated by real robot experiments with a 15 DoFs dual-arm manipulator.

Framework

Overview of the algorithm of the proposed method

HQP is the process of solving cascade numerical optimization problems using quadratic programming (QP). In the QP, we can minimize quadratic function while satisfying equality and inequality constraints. To reduce the computational cost of HQP controller, we propose a novel method that resizes the decision variables of the controller while satisfying a dynamical relatoinship of the rigid body.

Platform

Dual-arm manipulator (left) and schematic kinematic structure of the robot (right)

The 15-DoFs dual-arm manipulators have 7 DoFs for each arm and a 1 DoF prismatic joint for vertical motion. The HQP is solved by the library qpOASES, and rigid body dynamics parameters are obtained from the library RBDL and URDF model of the robot. Eigen library is utilized for linear algebra computation. The controller is implemented in the computer with Intel 3.1 GHz hexadecacore processor and 32 GByte memory with Linux and Xenomai for 1 kHz real-time control. For joint torque control, Elmo motor drivers are utilized with an EtherCAT communication interface.

Experimental Results

Computation time consumed with rHQP (blue), HQP (red), and OSF (yellow)	Statistical results of each method

For the comparison of performance, we conduct trajectory tracking experiments. Since the task for comparison is designed to compare the efficiency of computation, all controllers including rHQP, HQP, and operational space formulation (OSF) generate a similar control solution. As a result, rHQP solves about x2.44 faster than the conventional HQP on average.

Joint torque constraints of the wrist pitch joints and desired joint torque result

Although the computational cost of rHQP is lower than that of HQP, it is still higher than that of OSF. However, in contrast to OSF, rHQP can satisfy inequality constraints of optimal control problem. To verify this, we conduct an experiment whether rHQP can indeed satisfy joint torque inequality constraints. Our method successfully satisfy the inequality condition that the joint torque of wrist pitch should be bounded to narrow as -2.3 Nm ~ 2.3Nm. As a result, rHQP can solve optimization problem much faster than the previous methods without any sacrification of optimality of the solution.

Citation

Acknowledgements

This project was supported by the Korea Institute of Science, and Technology Institutional Programs under Grant 2E31593.

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