Body Schema Acquisition through Active Learning

TL;DR

The paper addresses online body schema learning for serial humanoid robots by combining Recursive Least Squares parameter estimation with an active learning strategy based on Bayesian experimental design. The method defines a cost via A-optimality that reduces to the posterior covariance trace, and selects the next configuration by efficiently minimizing this cost using DIRECT optimization, enabling real-time operation. Empirical results in simulation and on a real robot show that the approach converges faster and requires far fewer observations than gradient-based methods, thereby improving robustness and data efficiency for kinematic calibration. This work advances practical online calibration of robot kinematics by leveraging informative experiment design and fast linear-Gaussian updates.

Abstract

We present an active learning algorithm for the problem of body schema learning, i.e. estimating a kinematic model of a serial robot. The learning process is done online using Recursive Least Squares (RLS) estimation, which outperforms gradient methods usually applied in the literature. In addiction, the method provides the required information to apply an active learning algorithm to find the optimal set of robot configurations and observations to improve the learning process. By selecting the most informative observations, the proposed method minimizes the required amount of data. We have developed an efficient version of the active learning algorithm to select the points in real-time. The algorithms have been tested and compared using both simulated environments and a real humanoid robot.

Figures (7)

• Figure 1: (a) Humanoid robot with a binocular head and a 6 dof arm and (b) sketch of the body schema learning problem.
• Figure 2: Steps for the active selection of the most informative configurations.
• Figure 3: Example of an iteration of DIRECT for a 2D function. The division from the previous iteration is shown in a). We evaluate all the middle points and find the potentially optimal hypercubes (shaded). Then, we subdivide those hypercubes as shown in b) and iterate. The potentially optimal hypercubes are the points that fall in the lower convex hull shown in c), where $f(c_j)$ is the value of the function in the central point, and $d_j$ is the distance of the central point to the extreme. Adapted from Jones:1993.
• Figure 4: Convergence of the body schema learning for a $6$ dof robot. (a) mean error in the relative orientations of the joint angles, (b) mean error in the location of the joint angle and (c) prediction error during the learning. Each figure shows the results for random exploration using the RLS, the active approach and an stochastic gradient method.
• Figure 5: Convergence of the body schema learning for the simulated robot with $12$ dof. (a) mean error in the relative orientations of the joint angles, (b) mean error in the location of the joint angle and (c) prediction error during the learning. Each figure shows the results for random exploration using the RLS, the active approach and an stochastic gradient method.