Whole-body kinematic control of nonholonomic mobile manipulators using linear programming

Abstract

This work presents the study and implementation of the robot kinematic control strategy based on linear programming recently proposed by Gonçalves et al. (2016). In addition to being computationally efficient, this approach enables the inclusion of inequality and equality constraints in the system control inputs and has formal guarantee of stability. This method was applied to a nonholonomic mobile manipulator and some improvements were proposed to the original formulation, such as the addition of a new positive definite function of the error variation to avoid joint movements when the robot end effector stabilizes at a point different from the desired one. In addition, nonholonomic constraints of the mobile base are imposed as equality constraints in the linear program and therefore there is no need to use a cascade control structure to perform whole body control. Inequality constraints were also defined to avoid both violation of joint limits and collisions with obstacles. To guarantee a good performance, the controller was implemented on the Robot Operating System (ROS) using C++. In addition, a computer vision system based on RGB-D sensors for marker recognition was also integrated into the experimental testbed with the goal of improving robot localization and detecting obstacles in the workspace. In order to evaluate the controller performance, a comparison was made with a cascade control structure in which an inner loop is used to deal with the nonholonomic constraints of the mobile base by using an input-output linearization and an outer loop is used to tackle the whole-body motion by using the pseudoinverse of the whole-body Jacobian matrix. Simulation and experimental results show that the controller based on linear programming has low computational cost, and the robot is able to control its end effector without colliding with obstacles in the plane and without violating its joints limits. However, when using the Simplex algorithm the method based on linear programming generates more abrupt control signals than those generated by the cascade controller based on the pseudoinverse of the robot Jacobian matrix.