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The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often challenging or even infeasible due to the complexity of the system dynamics. In contrast, data-driven approaches need only a minimum of prior knowledge and scale with the complexity of the system. In particular, Gaussian process dynamical models (GPDMs) provide very promising results for the modeling of complex dynamics. However, the control properties of these GP models are just sparsely researched, which leads to a "blackbox" treatment in modeling and control scenarios. In addition, the sampling of GPDMs for prediction purpose respecting their non-parametric nature results in non-Markovian dynamics making the theoretical analysis challenging. In this article, we present approximated GPDMs which are Markov and analyze their control theoretical properties. Among others, the approximated error is analyzed and conditions for boundedness of the trajectories are provided. The outcomes are illustrated with numerical examples that show the power of the approximated models while the the computational time is significantly reduced.

We propose a method for jointly estimating the 3D motion, 3D shape, and appearance of highly motion-blurred objects from a video. To this end, we model the blurred appearance of a fast moving object in a generative fashion by parametrizing its 3D position, rotation, velocity, acceleration, bounces, shape, and texture over the duration of a predefined time window spanning multiple frames. Using differentiable rendering, we are able to estimate all parameters by minimizing the pixel-wise reprojection error to the input video via backpropagating through a rendering pipeline that accounts for motion blur by averaging the graphics output over short time intervals. For that purpose, we also estimate the camera exposure gap time within the same optimization. To account for abrupt motion changes like bounces, we model the motion trajectory as a piece-wise polynomial, and we are able to estimate the specific time of the bounce at sub-frame accuracy. Experiments on established benchmark datasets demonstrate that our method outperforms previous methods for fast moving object deblurring and 3D reconstruction.

Multi-robot systems offer enhanced capability over their monolithic counterparts, but they come at a cost of increased complexity in coordination. To reduce complexity and to make the problem tractable, multi-robot motion planning (MRMP) methods in the literature adopt de-coupled approaches that sacrifice either optimality or dynamic feasibility. In this paper, we present a convexification method, namely "parabolic relaxation", to generate optimal and dynamically feasible trajectories for MRMP in the coupled joint-space of all robots. We leverage upon the proposed relaxation to tackle the problem complexity and to attain computational tractability for planning over one hundred robots in extremely clustered environments. We take a multi-stage optimization approach that consists of i) mathematically formulating MRMP as a non-convex optimization, ii) lifting the problem into a higher dimensional space, iii) convexifying the problem through the proposed computationally efficient parabolic relaxation, and iv) penalizing with iterative search to ensure feasibility and recovery of feasible and near-optimal solutions to the original problem. Our numerical experiments demonstrate that the proposed approach is capable of generating optimal and dynamically feasible trajectories for challenging motion planning problems with higher success rate than the state-of-the-art, yet remain computationally tractable for over one hundred robots in a highly dense environment.

Task and motion planning problems in robotics typically combine symbolic planning over discrete task variables with motion optimization over continuous state and action variables, resulting in trajectories that satisfy the logical constraints imposed on the task variables. Symbolic planning can scale exponentially with the number of task variables, so recent works such as PDDLStream have focused on optimistic planning with an incrementally growing set of objects and facts until a feasible trajectory is found. However, this set is exhaustively and uniformly expanded in a breadth-first manner, regardless of the geometric structure of the problem at hand, which makes long-horizon reasoning with large numbers of objects prohibitively time-consuming. To address this issue, we propose a geometrically informed symbolic planner that expands the set of objects and facts in a best-first manner, prioritized by a Graph Neural Network based score that is learned from prior search computations. We evaluate our approach on a diverse set of problems and demonstrate an improved ability to plan in large or difficult scenarios. We also apply our algorithm on a 7DOF robotic arm in several block-stacking manipulation tasks.

This paper studies optimal motion planning subject to motion and environment uncertainties. By modeling the system as a probabilistic labeled Markov decision process (PL-MDP), the control objective is to synthesize a finite-memory policy, under which the agent satisfies high-level complex tasks expressed as linear temporal logic (LTL) with desired satisfaction probability. In particular, the cost optimization of the trajectory that satisfies infinite-horizon tasks is considered, and the trade-off between reducing the expected mean cost and maximizing the probability of task satisfaction is analyzed. Instead of using traditional Rabin automata, the LTL formulas are converted to limit-deterministic B\"uchi automata (LDBA) with a more straightforward accepting condition and a more compact graph structure. The novelty of this work lies in the consideration of the cases that LTL specifications can be potentially infeasible and the development of a relaxed product MDP between PL-MDP and LDBA. The relaxed product MDP allows the agent to revise its motion plan whenever the task is not fully feasible and to quantify the violation measurement of the revised plan. A multi-objective optimization problem is then formulated to jointly consider the probability of the task satisfaction, the violation with respect to original task constraints, and the implementation cost of the policy execution, which is solved via coupled linear programs. To the best of our knowledge, it is the first work that bridges the gap between planning revision and optimal control synthesis of both plan prefix and plan suffix of the agent trajectory over the infinite horizon. Experimental results are provided to demonstrate the effectiveness of the proposed framework.

Imitation learning enables agents to reuse and adapt the hard-won expertise of others, offering a solution to several key challenges in learning behavior. Although it is easy to observe behavior in the real-world, the underlying actions may not be accessible. We present a new method for imitation solely from observations that achieves comparable performance to experts on challenging continuous control tasks while also exhibiting robustness in the presence of observations unrelated to the task. Our method, which we call FORM (for "Future Observation Reward Model") is derived from an inverse RL objective and imitates using a model of expert behavior learned by generative modelling of the expert's observations, without needing ground truth actions. We show that FORM performs comparably to a strong baseline IRL method (GAIL) on the DeepMind Control Suite benchmark, while outperforming GAIL in the presence of task-irrelevant features.

Many important real-world problems have action spaces that are high-dimensional, continuous or both, making full enumeration of all possible actions infeasible. Instead, only small subsets of actions can be sampled for the purpose of policy evaluation and improvement. In this paper, we propose a general framework to reason in a principled way about policy evaluation and improvement over such sampled action subsets. This sample-based policy iteration framework can in principle be applied to any reinforcement learning algorithm based upon policy iteration. Concretely, we propose Sampled MuZero, an extension of the MuZero algorithm that is able to learn in domains with arbitrarily complex action spaces by planning over sampled actions. We demonstrate this approach on the classical board game of Go and on two continuous control benchmark domains: DeepMind Control Suite and Real-World RL Suite.

In this work, we present a method for tracking and learning the dynamics of all objects in a large scale robot environment. A mobile robot patrols the environment and visits the different locations one by one. Movable objects are discovered by change detection, and tracked throughout the robot deployment. For tracking, we extend the Rao-Blackwellized particle filter of previous work with birth and death processes, enabling the method to handle an arbitrary number of objects. Target births and associations are sampled using Gibbs sampling. The parameters of the system are then learnt using the Expectation Maximization algorithm in an unsupervised fashion. The system therefore enables learning of the dynamics of one particular environment, and of its objects. The algorithm is evaluated on data collected autonomously by a mobile robot in an office environment during a real-world deployment. We show that the algorithm automatically identifies and tracks the moving objects within 3D maps and infers plausible dynamics models, significantly decreasing the modeling bias of our previous work. The proposed method represents an improvement over previous methods for environment dynamics learning as it allows for learning of fine grained processes.

Querying graph structured data is a fundamental operation that enables important applications including knowledge graph search, social network analysis, and cyber-network security. However, the growing size of real-world data graphs poses severe challenges for graph databases to meet the response-time requirements of the applications. Planning the computational steps of query processing - Query Planning - is central to address these challenges. In this paper, we study the problem of learning to speedup query planning in graph databases towards the goal of improving the computational-efficiency of query processing via training queries.We present a Learning to Plan (L2P) framework that is applicable to a large class of query reasoners that follow the Threshold Algorithm (TA) approach. First, we define a generic search space over candidate query plans, and identify target search trajectories (query plans) corresponding to the training queries by performing an expensive search. Subsequently, we learn greedy search control knowledge to imitate the search behavior of the target query plans. We provide a concrete instantiation of our L2P framework for STAR, a state-of-the-art graph query reasoner. Our experiments on benchmark knowledge graphs including DBpedia, YAGO, and Freebase show that using the query plans generated by the learned search control knowledge, we can significantly improve the speed of STAR with negligible loss in accuracy.

Current convolutional neural networks algorithms for video object tracking spend the same amount of computation for each object and video frame. However, it is harder to track an object in some frames than others, due to the varying amount of clutter, scene complexity, amount of motion, and object's distinctiveness against its background. We propose a depth-adaptive convolutional Siamese network that performs video tracking adaptively at multiple neural network depths. Parametric gating functions are trained to control the depth of the convolutional feature extractor by minimizing a joint loss of computational cost and tracking error. Our network achieves accuracy comparable to the state-of-the-art on the VOT2016 benchmark. Furthermore, our adaptive depth computation achieves higher accuracy for a given computational cost than traditional fixed-structure neural networks. The presented framework extends to other tasks that use convolutional neural networks and enables trading speed for accuracy at runtime.