Whole-body self-calibration via graph-optimization and automatic configuration selection

Abstract

In this paper, we present a novel approach to accurately calibrate the kinematic model of a humanoid based on observations of its monocular camera. Our technique estimates the parameters of the complete model, consisting of the joint angle offsets of the whole body including the legs, as well as the camera extrinsic and intrinsic parameters. We cast the parameter estimation as a least-squares optimization problem. In the error function, we consider the residuals between camera observations of end-effector markers and their projections into the image based on the estimate of the calibration parameters. Furthermore, we developed an approach to automatically select a subset of configurations for the calibration process that yields a good trade-off between the number of observations and accuracy. As the experiments with a Nao humanoid show, we achieve an accurate calibration for this low-cost platform. Further, our approach to configuration selection yields substantially better optimization results compared to randomly chosen viable configurations. Hence, our system only requires a reduced number of configurations to achieve accurate results. Our optimization is general and the implementation, which is available online, can easily be applied to different humanoids.

Self-Contained Calibration of an Elastic Humanoid Upper Body Using Only a Head-Mounted RGB Camera

“…Maier et al [9] calibrated the joint offsets for the humanoid robot Nao by following four checkerboard markers on both of its hands and feet with its RGB camera. Finally, Stepanova et al [10] used a combination of visual and tactile self-observing to calibrate all the DH parameters for the iCub robot.…”

Integrated on-line robot-camera calibration and object pose estimation

“…These approaches however are still used to provide initial estimates for the more recent iterative approaches. The latter minimize a feature reprojection error in a similar way as bundle adjustment approaches in computer vision [2], [7], [10]. Our approach here relates to bundle adjustment in that the scene structure is part of the parameter space.…”

“…Although much progress has been made on this problem [3]- [5], visual robot pose estimation is still very difficult. The problem can be somewhat simplified by attaching markers to the robot [2], [6], [7] but this may not always be feasible and it is still difficult to estimate the 3D position of the marker in the camera frame accurately. For this reason, the less informative 2D image projection of the marker is typically used in the error formulation.…”

“…Recently there has also been work focusing specifically on the problem of selecting a set of configurations that maximizes the accuracy of the calibration while minimizing the calibration time [7], [11], [12]. These works do not consider on-line calibration and instead generate a batch of configurations that is checked for marker visibility and collision-free, and then subsample this batch before executing it on the robot.…”

“…At each time instance, the newly arriving sample is evaluated against all other samples in the configuration set in order to greedily maximize an observability index. In accordance with [7], [12] we use the following index:…”