This paper presents some improvements to the robot kinematic control strategy based on linear programming, as well as its application to a nonholonomic mobile manipulator. 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. We first propose 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, the nonholonomic constraint of the mobile base is imposed as an equality constraint, and inequality constraints are defined to avoid both violation of joint limits and collisions between the mobile base and obstacles in the plane. Last, a performance comparison between the linear programming strategy and an approach based on the pseudoinverse of the whole-body Jacobian matrix is presented. 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, it tends to generate more abrupt control signals than the continuous controller based on the pseudoinverse of the whole-body Jacobian matrix.