Recent anthropomorphic robots, most notably the one developed within the SENSOPAC project at DLR, feature a complex kinematic structure with many degrees of freedom (DOF). Consequently, the forward and inverse dynamics are very complicated, and an analytic derivation of these mappings is cumbersome, subject to approximations, or even impossible. Since an accurate model of the inverse dynamics is the key to precise, yet compliant control of the robot, it is desirable to learn such a model from data. More importantly, when learning an internal model of the dynamics, we can incorporate haptic information and therefore learn about the structure of the sensorimotor space. Furthermore, the model can be adapted to changes in the environment. Hereto, please also see our subproject Context Estimation and Switching.

Unfortunately, the inverse dynamics mapping (from the current state and the desired change to the necessary torques or motor commands) has a high input dimensionality (3 times the number of DOFs plus the haptic information), so many standard regression techniques designed for rather low dimensionalities fail.

Online learning in high dimensions

We develop non-parametric local weighted learning techniques, where we aim for robustness and the ability to learn in an online, incremental fashion. We approximate the global regression function by a mixture of multiple linear models, each of which is "responsible" in a certain region as determined by a center and an automatically adapted distance metrics. The local regression models are learned using partial least squares, and leave-one-out cross-validation is utilized for ongoing assessment and complexity control of the model. Local models can be added and purged as required during training [1].

Bayesian treatment of open parameters

We investigate Bayesian methods to address the problem of open parameters like learning rates, forgetting factors, and initial distance metrics. By formulating a novel Randomly Varying Coefficient model, we bring together two separate lines of research: we combine the efficiency of non-competitive locally weighted learning schemes with the recognised modelling strength of Bayesian approaches [2].

SENSOPAC Deliverables

As a deliverable (D2.6) for the SENSOPAC project, we will release a software package for regression that includes appropiate documentation and routines in MATLAB and C++. The underlying algorithm of that software package will be LWPR (Locally Weighted Projection Regression), which has matured over several years in our group.

While our learning algorithms are applicable for general purposes, within SENSOPAC the most important field of application is its deployment for internal model based control of a robot arm. We will also spent effort to unify our online learning algorithm with the (classical) control strategies currently used at the DLR labs.

Related Publications

[1]

Vijayakumar, S., D'Souza, A., & Schaal, S., Incremental Online Learning in High Dimensions. Neural Computation, vol. 17, no. 12, pp. 2602-2634 (2005). [pdf]

[2]

Narayanan, U.E., Schaal, S., & Vijayakumar, S., Kernel Carpentry for Online Regression using Randomly Varying Coefficient Model. International Joint Conference in AI (IJCAI) Hyderabad, India (2007). [pdf]