During the past few years, probabilistic approaches to imitation learning have earned a relevant place in the literature. One of their most prominent features, in addition to extracting a mean trajectory from task demonstrations, is that they provide a variance estimation. The intuitive meaning of this variance, however, changes across different techniques, indicating either variability or uncertainty. In this paper we leverage kernelized movement primitives (KMP) to provide a new perspective on imitation learning by predicting variability, correlations and uncertainty about robot actions. This rich set of information is used in combination with optimal controller fusion to learn actions from data, with two main advantages: i) robots become safe when uncertain about their actions and ii) they are able to leverage partial demonstrations, given as elementary sub-tasks, to optimally perform a higher level, more complex task. We showcase our approach in a painting task, where a human user and a KUKA robot collaborate to paint a wooden board. The task is divided into two sub-tasks and we show that using our approach the robot becomes compliant (hence safe) outside the training regions and executes the two sub-tasks with optimal gains.
In terms of estimating optimal controllers from demonstrations, previous works have either exploited full covariance matrices encoding variability and correlations @cite_5 @cite_19 @cite_12 @cite_14 or diagonal uncertainty matrices @cite_25 . While the former are aimed at control efficiency, by having the robot apply higher control efforts where required depending on variability, the latter target safety with the robot becoming more compliant when uncertain about its actions. The LQR we propose in Section is identical to the one in @cite_5 @cite_25 @cite_12 however, by benefiting from the KMP predictions, it unifies the best of the two approaches.
@cite_14 @cite_19 @cite_5 @cite_25 @cite_12
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While human behavior prediction can increase the capability of a robotic partner to generate anticipatory behavior during physical human robot interaction (pHRI), predictions in uncertain situations can lead to large disturbances for the human if they do not match the human intentions. In this paper we present a novel control concept in which the assistive control parameters are adapted to the uncertainty in the sense that a the robot takes a more or less active role depending on its confidence in the human behavior prediction. The approach is based on risk-sensitive optimal feedback control. The human behavior is modeled using probabilistic learning methods and any unexpected disturbance is considered as a source of noise. The proposed approach is validated in situations with different uncertainties, process noise and risk-sensitivities in a tow- Degree-of-Freedom virtual reality experiment. We present a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame at each step of the task. This information is exploited to generate new attractor paths in new situations (new position and orientation of the frames), with the predicted covariances used to estimate the varying stiffness and damping of the spring-damper systems, resulting in a minimal intervention control strategy. The approach is tested with a 7-DOFs Barrett WAM manipulator whose movement and impedance behavior need to be modulated in regard to the position and orientation of two external objects varying during demonstration and reproduction. Motivated by the desire to have robots physically present in human environments, in recent years we have witnessed an emergence of different approaches for learning active compliance. Some of the most compelling solutions exploit a minimal intervention control principle, correcting deviations from a goal only when necessary, and among those who follow this concept, several probabilistic techniques have stood out from the rest. However, these approaches are prone to requiring several task demonstrations for proper gain estimation and to generating unpredictable robot motions in the face of uncertainty. Here we present a Programming by Demonstration approach for uncertainty-aware impedance regulation, aimed at making the robot compliant - and safe to interact with - when the uncertainty about its predicted actions is high. Moreover, we propose a data-efficient strategy, based on the energy observed during demonstrations, to achieve minimal intervention control, when the uncertainty is low. The approach is validated in an experimental scenario, where a human collaboratively moves an object with a 7-DoF torque-controlled robot. Human-robot collaboration seeks to have humans and robots closely interacting in everyday situations. For some tasks, physical contact between the user and the robot may occur, originating significant challenges at safety, cognition, perception and control levels, among others. This paper focuses on robot motion adaptation to parameters of a collaborative task, extraction of the desired robot behavior, and variable impedance control for human-safe interaction. We propose to teach a robot cooperative behaviors from demonstrations, which are probabilistically encoded by a task-parametrized formulation of a Gaussian mixture model. Such encoding is later used for specifying both the desired state of the robot, and an optimal feedback control law that exploits the variability in position, velocity and force spaces observed during the demonstrations. The whole framework allows the robot to modify its movements as a function of parameters of the task, while showing different impedance behaviors. Tests were successfully carried out in a scenario where a 7 DOF backdrivable manipulator learns to cooperate with a human to transport an object.