In this work, we present a sampling-based approach to trajectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the pathconnectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2, 3, 4 and 6 dimensional configuration spaces in simulation and in real-world experiments using a Baxter robot and motion capture data 1 .

A long-lived autonomous agent should be able to respond online to novel instances of tasks from a familiar domain. Acting online requires 'fast' responses, in terms of rapid convergence, especially when the task instance has a short duration such as in applications involving interactions with humans. These requirements can be problematic for many established methods for learning to act. In domains where the agent knows that the task instance is drawn from a family of related tasks, albeit without access to the label of any given instance, it can choose to act through a process of policy reuse from a library in contrast to policy learning. In policy reuse, the agent has prior experience from the class of tasks in the form of a library of policies that were learnt from sample task instances during an offline training phase. We formalise the problem of policy reuse and present an algorithm for efficiently responding to a novel task instance by reusing a policy from this library of existing policies, where the choice is based on observed 'signals' which correlate to policy performance. We achieve this by posing the problem as a Bayesian choice problem with a corresponding notion of an optimal response, but the computation of that response is in many cases intractable. Therefore, to reduce the computation cost of the posterior, we follow a Bayesian optimisaEditor: Peter Flach.Benjamin Rosman and Majd Hawasly have contributed equally to this paper. 123Mach Learn tion approach and define a set of policy selection functions, which balance exploration in the policy library against exploitation of previously tried policies, together with a model of expected performance of the policy library on their corresponding task instances. We validate our method in several simulated domains of interactive, short-duration episodic tasks, showing rapid convergence in unknown task variations.

Recent road trials have shown that guaranteeing the safety of driving decisions is essential for the wider adoption of autonomous vehicle technology. One promising direction is to pose safety requirements as planning constraints in nonlinear, non-convex optimization problems of motion synthesis. However, many implementations of this approach are limited by uncertain convergence and local optimality of the solutions achieved, affecting overall robustness. To improve upon these issues, we propose a novel two-stage optimization framework: in the first stage, we find a solution to a Mixed-Integer Linear Programming (MILP) formulation of the motion synthesis problem, the output of which initializes a second Nonlinear Programming (NLP) stage. The MILP stage enforces hard constraints of safety and road rule compliance generating a solution in the right subspace, while the NLP stage refines the solution within the safety bounds for feasibility and smoothness. We demonstrate the effectiveness of our framework via simulated experiments of complex urban driving scenarios, outperforming a state-of-the-art baseline in metrics of convergence, comfort and progress.

Abstract-Topological approaches to studying equivalence classes of trajectories in a configuration space have recently received attention in robotics since they allow a robot to reason about trajectories at a high level of abstraction. While recent work has approached the problem of topological motion planning under the assumption that the configuration space and obstacles within it are explicitly described in a noise-free manner, we focus on trajectory classification and present a samplingbased approach which can handle noise, which is applicable to general configuration spaces and which relies only on the availability of collision free samples. Unlike previous samplingbased approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. By computing a basis for the first persistent homology groups, we obtain a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension. We furthermore show how an augmented filtration of simplicial complexes based on a cost function can be defined to incorporate additional constraints. We present an evaluation of our approach in 2, 3, 4 and 6 dimensional configuration spaces in simulation and using a Baxter robot.

Deep Neural Networks (DNNs) are finding important applications in safety-critical systems such as Autonomous Vehicles (AVs), where perceiving the environment correctly and robustly is necessary for safe operation. Raising unique challenges for assurance due to their black-box nature, DNNs pose a fundamental problem for regulatory acceptance of these types of systems. Robust training -training to minimize excessive sensitivity to small changes in input -has emerged as one promising technique to address this challenge. However, existing robust training tools are inconvenient to use or apply to existing codebases and models: they typically only support a small subset of model elements and require users to extensively rewrite the training code. In this paper we introduce a novel framework, PaRoT, developed on the popular TensorFlow platform, that greatly reduces the barrier to entry. Our framework enables robust training to be performed on existing DNNs without rewrites to the model. We demonstrate that our framework's performance is comparable to prior art, and exemplify its ease of use on off-the-shelf, trained models and its testing capabilities on a realworld industrial application: a traffic light detection network.