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Automated vehicles require the ability to cooperate with humans for smooth integration into today's traffic. While the concept of cooperation is well known, developing a robust and efficient cooperative trajectory planning method is still a challenge. One aspect of this challenge is the uncertainty surrounding the state of the environment due to limited sensor accuracy. This uncertainty can be represented by a Partially Observable Markov Decision Process. Our work addresses this problem by extending an existing cooperative trajectory planning approach based on Monte Carlo Tree Search for continuous action spaces. It does so by explicitly modeling uncertainties in the form of a root belief state, from which start states for trees are sampled. After the trees have been constructed with Monte Carlo Tree Search, their results are aggregated into return distributions using kernel regression. We apply two risk metrics for the final selection, namely a Lower Confidence Bound and a Conditional Value at Risk. It can be demonstrated that the integration of risk metrics in the final selection policy consistently outperforms a baseline in uncertain environments, generating considerably safer trajectories.

Free-space-oriented roadmaps typically generate a series of convex geometric primitives, which constitute the safe region for motion planning. However, a static environment is assumed for this kind of roadmap. This assumption makes it unable to deal with dynamic obstacles and limits its applications. In this paper, we present a dynamic free-space roadmap, which provides feasible spaces and a navigation graph for safe quadrotor motion planning. Our roadmap is constructed by continuously seeding and extracting free regions in the environment. In order to adapt our map to environments with dynamic obstacles, we incrementally decompose the polyhedra intersecting with obstacles into obstacle-free regions, while the graph is also updated by our well-designed mechanism. Extensive simulations and real-world experiments demonstrate that our method is practically applicable and efficient.

Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of networks of connected GP emulators. In this paper, we combine these recent methodological advances with classical state-space models to construct a Bayesian decision support system. This approach gives a coherent probability model that produces predictions with the measure of uncertainty in terms of two first moments and enables the propagation of uncertainty from individual decision components. This methodology is used to produce a decision support tool for a UK county council considering low carbon technologies to transform its infrastructure to reach a net-zero carbon target. In particular, we demonstrate how to couple information from an energy model, a heating demand model, and gas and electricity price time-series to quantitatively assess the impact on operational costs of various policy choices and changes in the energy market.

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental problem in the framework of energy-based model, where the observed expert trajectories are assumed to be random samples from a probability density function defined as the exponential of the negative cost function up to a normalizing constant. The parameters of the cost function are learned by maximum likelihood via an "analysis by synthesis" scheme, which iterates (1) synthesis step: sample the synthesized trajectories from the current probability density using the Langevin dynamics via back-propagation through time, and (2) analysis step: update the model parameters based on the statistical difference between the synthesized trajectories and the observed trajectories. Given the fact that an efficient optimization algorithm is usually available for an optimal control problem, we also consider a convenient approximation of the above learning method, where we replace the sampling in the synthesis step by optimization. Moreover, to make the sampling or optimization more efficient, we propose to train the energy-based model simultaneously with a top-down trajectory generator via cooperative learning, where the trajectory generator is used to fast initialize the synthesis step of the energy-based model. We demonstrate the proposed methods on autonomous driving tasks, and show that they can learn suitable cost functions for optimal control.

Approximate Policy Iteration (API) algorithms alternate between (approximate) policy evaluation and (approximate) greedification. Many different approaches have been explored for approximate policy evaluation, but less is understood about approximate greedification and what choices guarantee policy improvement. In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization. We show that the reverse KL has stronger policy improvement guarantees, but that reducing the forward KL can result in a worse policy. We also demonstrate, however, that a large enough reduction of the forward KL can induce improvement under additional assumptions. Empirically, we show on simple continuous-action environments that the forward KL can induce more exploration, but at the cost of a more suboptimal policy. No significant differences were observed in the discrete-action setting or on a suite of benchmark problems. Throughout, we highlight that many policy gradient methods can be seen as an instance of API, with either the forward or reverse KL for the policy update, and discuss next steps for understanding and improving our policy optimization algorithms.

This paper presents a hybrid robot motion planner that generates long-horizon motion plans for robot navigation in environments with obstacles. We propose a hybrid planner, RRT* with segmented trajectory optimization (RRT*-sOpt), which combines the merits of sampling-based planning, optimization-based planning, and trajectory splitting to quickly plan for a collision-free and dynamically-feasible motion plan. When generating a plan, the RRT* layer quickly samples a semi-optimal path and sets it as an initial reference path. Then, the sOpt layer splits the reference path and performs optimization on each segment. It then splits the new trajectory again and repeats the process until the whole trajectory converges. We also propose to reduce the number of segments before convergence with the aim of further reducing computation time. Simulation results show that RRT*-sOpt benefits from the hybrid structure with trajectory splitting and performs robustly in various robot platforms and scenarios.

As technology advances, the need for safe, efficient, and collaborative human-robot-teams has become increasingly important. One of the most fundamental collaborative tasks in any setting is the object handover. Human-to-robot handovers can take either of two approaches: (1) direct hand-to-hand or (2) indirect hand-to-placement-to-pick-up. The latter approach ensures minimal contact between the human and robot but can also result in increased idle time due to having to wait for the object to first be placed down on a surface. To minimize such idle time, the robot must preemptively predict the human intent of where the object will be placed. Furthermore, for the robot to preemptively act in any sort of productive manner, predictions and motion planning must occur in real-time. We introduce a novel prediction-planning pipeline that allows the robot to preemptively move towards the human agent's intended placement location using gaze and gestures as model inputs. In this paper, we investigate the performance and drawbacks of our early intent predictor-planner as well as the practical benefits of using such a pipeline through a human-robot case study.

The problem of active mapping aims to plan an informative sequence of sensing views given a limited budget such as distance traveled. This paper consider active occupancy grid mapping using a range sensor, such as LiDAR or depth camera. State-of-the-art methods optimize information-theoretic measures relating the occupancy grid probabilities with the range sensor measurements. The non-smooth nature of ray-tracing within a grid representation makes the objective function non-differentiable, forcing existing methods to search over a discrete space of candidate trajectories. This work proposes a differentiable approximation of the Shannon mutual information between a grid map and ray-based observations that enables gradient ascent optimization in the continuous space of SE(3) sensor poses. Our gradient-based formulation leads to more informative sensing trajectories, while avoiding occlusions and collisions. The proposed method is demonstrated in simulated and real-world experiments in 2-D and 3-D environments.

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.

Recent advances in sensor and mobile devices have enabled an unprecedented increase in the availability and collection of urban trajectory data, thus increasing the demand for more efficient ways to manage and analyze the data being produced. In this survey, we comprehensively review recent research trends in trajectory data management, ranging from trajectory pre-processing, storage, common trajectory analytic tools, such as querying spatial-only and spatial-textual trajectory data, and trajectory clustering. We also explore four closely related analytical tasks commonly used with trajectory data in interactive or real-time processing. Deep trajectory learning is also reviewed for the first time. Finally, we outline the essential qualities that a trajectory management system should possess in order to maximize flexibility.