A method for robot placement optimization based on two-dimensional manifold in joint space

•A new method for robot placement optimization is proposed to improve the efficiency of two-dimensional error compensation.•The bifurcations which exist in two-dimensional manifolds are clearly explained with the kinematic model.•A quantitative index combined with Particle Swarm Optimization (PSO) is proposed to access the two-dimensional manifold.•The feasibility of proposed method is validated by positioning error experiments conducted on a typical industrial robot.•The whole process of placement optimization can be performed with the help of the integrated controlling system quickly.