Autonomous exploration is a complex task where the robot moves through an unknown environment with the goal of mapping it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of the resulting map. However, optimising over the entire space of possible paths is computationally intractable. Therefore, most exploration methods relax the general problem by optimising a simpler one, for example finding the single next best view. In this work, we formulate exploration as a variational problem which allows us to directly optimise in the space of trajectories using functional gradient methods, searching for the Next Best Path (NBP). We take advantage of the recently introduced Hilbert maps to devise an information-based functional that can be computed in closed-form. The resulting trajectories are continuous and maximise safety as well as mutual information. In experiments we verify the ability of the proposed method to find smooth and safe paths and compare these results with other exploration methods.
Information-theoretic exploration methods optimise a utility function associated with the uncertainty of the map. Early work optimised the selection of a discrete goal point rather than optimising an entire path. Elfes @cite_14 suggested MI as an information metric for exploration, while @cite_3 proposed a (NBV) approach using the entire map entropy. Vallv 'e and Andrade-Cetto @cite_15 use a potential field computed over the entire configuration space to find exploration candidates. However, this method assumes discrete steps, disregarding the reduction in entropy between consecutive robot poses. @cite_26 combined frontier and information-based methods. While they optimised the information heuristic over a continuous control input space, in effect the path consisted of a fixed number of time steps. Lauri and Ritala @cite_25 formulate the exploration problem as (POMDP) and used sample-based approach to solve the POMDP. Similarly to the work of @cite_26 , the action space is continuous, however, the path consists of a finite set of time steps, which is in contrast to the proposed method where optimisation is performed in the space of trajectories.
@cite_14 @cite_26 @cite_3 @cite_15 @cite_25
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This paper presents a generic approach for tactical decision-making under uncertainty in the context of driving. The complexity of this task mainly stems from the fact that rational decision-making in this context must consider several sources of uncertainty: The temporal evolution of situations cannot be predicted without uncertainty because other road users behave stochastically and their goals and plans cannot be measured. Even more important, road users are only able to perceive a tiny part of the current situation with their sensors because measurements are noisy and most of the environment is occluded. In order to anticipate the consequences of decisions a probabilistic approach, considering both forms of uncertainty, is necessary. The authors address this by formulating the task of driving as a continuous Partially Observable Markov Decision Process (POMDP) that can be automatically optimized for different scenarios. As driving is a continuous-space problem, the belief space is infinite-dimensional. The authors do not use a symbolic representation or discretize the state space a priori because there is no representation of the state space that is optimal for every situation. Instead, they employ a continuous POMDP solver that learns a good representation of the specific situation. Abstract We address the problem of controlling a mobile robot to explore a partially known environment. The robot’s objective is the maximization of the amount of information collected about the environment. We formulate the problem as a partially observable Markov decision process (POMDP) with an information-theoretic objective function, and solve it applying forward simulation algorithms with an open-loop approximation. We present a new sample-based approximation for mutual information useful in mobile robotics. The approximation can be seamlessly integrated with forward simulation planning algorithms. We investigate the usefulness of POMDP based planning for exploration, and to alleviate some of its weaknesses propose a combination with frontier based exploration. Experimental results in simulated and real environments show that, depending on the environment, applying POMDP based planning for exploration can improve performance over frontier exploration. We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng (1999), but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method applies to arbitrary POMDPs, including ones with infinite state and action spaces. We also present empirical results for our approach on a small discrete problem, and on a complex continuous state continuous action problem involving learning to ride a bicycle. We propose an information-theoretic planning approach that enables mobile robots to autonomously construct dense 3D maps in a computationally efficient manner. Inspired by prior work, we accomplish this task by formulating an information-theoretic objective function based on CauchySchwarz quadratic mutual information (CSQMI) that guides robots to obtain measurements in uncertain regions of the map. We then contribute a two stage approach for active mapping. First, we generate a candidate set of trajectories using a combination of global planning and generation of local motion primitives. From this set, we choose a trajectory that maximizes the information-theoretic objective. Second, we employ a gradientbased trajectory optimization technique to locally refine the chosen trajectory such that the CSQMI objective is maximized while satisfying the robot’s motion constraints. We evaluated our approach through a series of simulations and experiments on a ground robot and an aerial robot mapping unknown 3D environments. Real-world experiments suggest our approach reduces the time to explore an environment by 70 compared to a closest frontier exploration strategy and 57 compared to an information-based strategy that uses global planning, while simulations demonstrate the approach extends to aerial robots with higher-dimensional state.