Many practical tasks in robotic systems, such as cleaning windows, writing, or grasping, are inherently constrained. Learning policies subject to constraints is a challenging problem. In this paper, we propose a method of constraint-aware learning that solves the policy learning problem using redundant robots that execute a policy that is acting in the null space of a constraint. In particular, we are interested in generalizing learned null-space policies across constraints that were not known during the training. We split the combined problem of learning constraints and policies into two: first estimating the constraint, and then estimating a null-space policy using the remaining degrees of freedom. For a linear parametrization, we provide a closed-form solution of the problem. We also define a metric for comparing the similarity of estimated constraints, which is useful to pre-process the trajectories recorded in the demonstrations. We have validated our method by learning a wiping task from human demonstration on flat surfaces and reproducing it on an unknown curved surface using a force-or torque-based controller to achieve tool alignment. We show that, despite the differences between the training and validation scenarios, we learn a policy that still provides the desired wiping motion.

The analysis, design, and motion planning of robotic systems, often relies on its forward and inverse dynamic models. When executing a task involving interaction with the environment, both the task and the environment impose constraints on the robot's motion. For modeling such systems, we need to incorporate these constraints in the robot's dynamic model. In this paper, we define the class of Task-based Constraints (TbC) to prove that the forward dynamic models of a constrained system obtained through the Projection-based Dynamics (PbD), and the Operational Space Formulation (OSF) are equivalent. In order to establish such equivalence, we first generalize the OSF to a rank deficient Jacobian. This generalization allow us to numerically handle redundant constraints and singular configurations, without having to use different controllers in the vicinity of such configurations. We then reformulate the PbD constraint inertia matrix, generalizing all its previous distinct algebraic variations. We also analyse the condition number of different constraint inertia matrices, which affects the numerical stability of its inversion. Furthermore, we show that we can recover the operational space control with constraints from a multiple Task-based Constraint abstraction.

In this letter we present a control and trajectory tracking approach for wiping the train cab front panels, using a velocity controlled robotic manipulator and a force/torque sensor attached to its end effector, without using any surface model or vision-based surface detection. The control strategy consists in a simultaneous position and force controller, adapted from the operational space formulation, that aligns the cleaning tool with the surface normal, maintaining a set-point normal force, while simultaneously moving along the surface. The trajectory tracking strategy consists in specifying and tracking a two dimensional path that, when projected onto the train surface, corresponds to the desired pattern of motion. We first validated our approach using the Baxter robot to wipe a highly curved surface with both a spiral and a raster scan motion patterns. Finally, we implemented the same approach in a scaled robot prototype, specifically designed by ourselves to wipe a 1/8 scaled version of a train cab front, using a raster scan pattern.

Abstract-Many practical tasks in robotic systems, such as cleaning windows, writing or grasping, are inherently constrained. Learning policies subject to constraints is a challenging problem. We propose a locally weighted constrained projection learning method (LWCPL) that first estimates the constraint and then exploits this estimate across multiple observations of the constrained motion to learn an unconstrained policy. The generalization is achieved by projecting the unconstrained policy onto a new, previously unseen, constraint. We do not require any prior knowledge about the task or the policy, so we can use generic regressors to model the task and the policy. However, any prior beliefs about the structure of the motion can be expressed by choosing task-specific regressors. In particular, we can use robot kinematics and motion priors to improve the accuracy. Our evaluation results show that LWCPL outperform the state of the art method in accuracy of learning the constraints as well as the unconstrained policy, even in noisy conditions. We have validated our method by learning a wiping task from human demonstration on flat surfaces and reproducing it on an unknown curved surface using a force/torque based controller to achieve tool alignment. We show that, despite of the differences between the training and validation scenarios, we learn a policy that still provides the desired wiping motion.