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Kay Hansel, Julen Urain, Jan Peters, Georgia Chalvatzaki

Motion generation in cluttered, dense, and dynamic environments is a central topic in robotics, rendered as a multi-objective decision-making problem. Current approaches trade-off between safety and performance. On the one hand, reactive policies guarantee fast response to environmental changes at the risk of suboptimal behavior. On the other hand, planning-based motion generation provides feasible trajectories, but the high computational cost may limit the control frequency and thus safety. To combine the benefits of reactive policies and planning, we propose a hierarchical motion generation method. Moreover, we adopt probabilistic inference methods to formalize the hierarchical model and stochastic optimization. We realize this approach as a weighted product of stochastic, reactive expert policies, where planning is used to adaptively compute the optimal weights over the task horizon. This stochastic optimization avoids local optima and proposes feasible reactive plans that find paths in cluttered and dense environments. Our extensive experimental study in planar navigation and 6DoF manipulation shows that our proposed hierarchical motion generation method outperforms both myopic reactive controllers and online re-planning methods.

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Julen Urain, Niklas Funk, Jan Peters, Georgia Chalvatzaki

Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.

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Julen Urain, Niklas Funk, Georgia Chalvatzaki, Jan Peters

Multi-objective high-dimensional motion optimization problems are ubiquitous in robotics and highly benefit from informative gradients. To this end, we require all cost functions to be differentiable. We propose learning task-space, data-driven cost functions as diffusion models. Diffusion models represent expressive multimodal distributions and exhibit proper gradients over the entire space. We exploit these properties for motion optimization by integrating the learned cost functions with other potentially learned or hand-tuned costs in a single objective function and optimize all of them jointly by gradient descent. We showcase the benefits of joint optimization in a set of complex grasp and motion planning problems and compare against hierarchical approaches that decouple grasp selection from motion optimization.

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Alexander Lambert, An T. Le, Julen Urain, Georgia Chalvatzaki, Byron Boots, Jan Peters

In this paper, we focus on the problem of integrating Energy-based Models (EBM) as guiding priors for motion optimization. EBMs are a set of neural networks that can represent expressive probability density distributions in terms of a Gibbs distribution parameterized by a suitable energy function. Due to their implicit nature, they can easily be integrated as optimization factors or as initial sampling distributions in the motion optimization problem, making them good candidates to integrate data-driven priors in the motion optimization problem. In this work, we present a set of required modeling and algorithmic choices to adapt EBMs into motion optimization. We investigate the benefit of including additional regularizers in the learning of the EBMs to use them with gradient-based optimizers and we present a set of EBM architectures to learn generalizable distributions for manipulation tasks. We present multiple cases in which the EBM could be integrated for motion optimization and evaluate the performance of learned EBMs as guiding priors for both simulated and real robot experiments.

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Jascha Hellwig, Mark Baierl, Joao Carvalho, Julen Urain, Jan Peters

Creating mobile robots which are able to find and manipulate objects in large environments is an active topic of research. These robots not only need to be capable of searching for specific objects but also to estimate their poses often relying on environment observations, which is even more difficult in the presence of occlusions. Therefore, to tackle this problem we propose a simple hierarchical approach to estimate the pose of a desired object. An Active Visual Search module operating with RGB images first obtains a rough estimation of the object 2D pose, followed by a more computationally expensive Active Pose Estimation module using point cloud data. We empirically show that processing image features to obtain a richer observation speeds up the search and pose estimation computations, in comparison to a binary decision that indicates whether the object is or not in the current image.

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Julen Urain, Davide Tateo, Jan Peters

Learning robot motions from demonstration requires having models that are able to represent vector fields for the full robot pose when the task is defined in operational space. Recent advances in reactive motion generation have shown that it is possible to learn adaptive, reactive, smooth, and stable vector fields. However, these approaches define a vector field on a flat Euclidean manifold, while representing vector fields for orientations required to model the dynamics in non-Euclidean manifolds, such as Lie Groups. In this paper, we present a novel vector field model that can guarantee most of the properties of previous approaches i.e., stability, smoothness, and reactivity beyond the Euclidean space. In the experimental evaluation, we show the performance of our proposed vector field model to learn stable vector fields for full robot poses as SE(2) and SE(3) in both simulated and real robotics tasks.

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Julen Urain, Anqi Li, Puze Liu, Carlo D'Eramo, Jan Peters

Reactive motion generation problems are usually solved by computing actions as a sum of policies. However, these policies are independent of each other and thus, they can have conflicting behaviors when summing their contributions together. We introduce Composable Energy Policies (CEP), a novel framework for modular reactive motion generation. CEP computes the control action by optimization over the product of a set of stochastic policies. This product of policies will provide a high probability to those actions that satisfy all the components and low probability to the others. Optimizing over the product of the policies avoids the detrimental effect of conflicting behaviors between policies choosing an action that satisfies all the objectives. Besides, we show that CEP naturally adapts to the Reinforcement Learning problem allowing us to integrate, in a hierarchical fashion, any distribution as prior, from multimodal distributions to non-smooth distributions and learn a new policy given them.

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Julen Urain, Davide Tateo, Tianyu Ren, Jan Peters

We present a new family of deep neural network-based dynamic systems. The presented dynamics are globally stable and can be conditioned with an arbitrary context state. We show how these dynamics can be used as structured robot policies. Global stability is one of the most important and straightforward inductive biases as it allows us to impose reasonable behaviors outside the region of the demonstrations.

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Julen Urain, Michelle Ginesi, Davide Tateo, Jan Peters

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations. We prove the Lyapunov stability for a class of Stochastic Differential Equations and we propose a learning algorithm to learn them from a set of demonstrated trajectories. Our model extends the set of stable dynamical systems that can be represented by state-of-the-art approaches, eliminates the Gaussian assumption on the demonstrations, and outperforms the previous algorithms in terms of representation accuracy. We show the effectiveness of our method with both standard datasets and a real robot experiment.

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Julen Urain, Jan Peters

Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing, Probabilistic Theory field, Topology field or Statistics field.Anyway, up to now, none of the trajectory similarity measurements metrics are invariant to all possible linear transformation of the trajectories (rotation, scaling, reflection, shear mapping or squeeze mapping). Also not all of them are robust in front of noisy signals or fast enough for real-time trajectory classification. To overcome this limitation this paper proposes a similarity distance metric that will remain invariant in front of any possible linear transformation.Based on Pearson Correlation Coefficient and the Coefficient of Determination, our similarity metric, the Generalized Multiple Correlation Coefficient (GMCC) is presented like the natural extension of the Multiple Correlation Coefficient. The motivation of this paper is two fold. First, to introduce a new correlation metric that presents the best properties to compute similarities between trajectories invariant to linear transformations and compare it with some state of the art similarity distances.Second, to present a natural way of integrating the similarity metric in an Imitation Learning scenario for clustering robot trajectories.

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