New closed-form solution for kinematic parameter identification of a binocular head using point measurements

This paper proposes a new closed-form solution for identifying the kinematic parameters of an active binocular head having four revolute joints and two prismatic joints by using three-dimensional (3-D) point (position) measurements of a calibration point. Since this binocular head is composed of off-the-shelf components, its kinematic parameters are unknown. Therefore, we can not directly apply those existing nonlinear optimization methods. Even if we want to use the nonlinear optimization methods, a closed-form solution can be first applied to obtain accurate enough initial values. Hence, this paper considers only methods that provide closed-form solutions, i.e., those requiring no initial estimates. Notice that most existing closed-form solutions require pose (i.e., both position and orientation) measurements. However, as far as we know, there is no inexpensive technique which can provide accurate pose measurements. Therefore, existing closed-form solutions based on pose measurements can not give us the required accuracy. As a result, we have developed a new method that does not require orientation measurements and can use only the position measurements of a calibration point to obtain highly accurate estimates of kinematic parameters using closed-form solutions. The proposed method is based on the complete and parametrically continuous (CPC) kinematic model, and can be applied to any kind of kinematic parameter identification problems with or without multiple end-effecters, providing that the links are rigid, the joints are either revolute or prismatic and no closed-loop kinematic chain is included.