Information Theoretic Active Exploration in Signed Distance Fields

Active Exploration and Mapping via Iterative Covariance Regulation over Continuous SE(3) Trajectories

“…Namely, we have lim κ→+0 Φ(x) = He(x), where He(x) is the Heaviside function, also known as the unit step function. Using the function (20), we formulate (19) as:…”

“…Efficient computation methods have been proposed in [3] for Causchy-Schwarz quadratic mutual information (CSQMI), and in [4] for fast Shannon mutual information (FSMI). Instead of binary occupancy grid mapping, recent information-based active mapping techniques have considered truncated signed distance field (TSDF) maps [20] and multi-category semantic maps [21]. Existing methods are, however, limited to discrete control spaces, typically arXiv:2103.05819v1 [cs.RO] 10 Mar 2021 with a finite number of possible control inputs [22], [20], [3], [4], and have not considered optimal control formulations of the active mapping problem.…”

Active SLAM over Continuous Trajectory and Control: A Covariance-Feedback Approach

“…Efficient computation methods for computing uncertainty of volumetric maps have been proposed in [9] for Cauchy-Schwarz quadratic mutual information (CSQMI), and in [10] for fast Shannon mutual information (FSMI). Active mapping for truncated signed distance field (TSDF) reconstruction has been considered in [11] and multi-category semantic maps have been studied in [12]. Existing methods are, however, limited to discrete control spaces, typically with a finite number of possible control inputs, such as [11], [9], [10].…”

“…Active mapping for truncated signed distance field (TSDF) reconstruction has been considered in [11] and multi-category semantic maps have been studied in [12]. Existing methods are, however, limited to discrete control spaces, typically with a finite number of possible control inputs, such as [11], [9], [10]. Recently, in [13], we have developed a continuous trajectory optimization method for active mapping, named iterative Covariance Regulation (iCR).…”

“…A major advantage of the proposed method is its ability to capture the coupling between localization and mapping in predicting uncertainty evolution and to synthesize highly informative sensing trajectories due to the continuous-space optimization, which is computationally efficient and capable of real-time implementation through an offline computation. We first provide a general formulation of the active information acquisition as studied in [25], [11], [13]. Apart from the previous literature, we include a stochastic process noise in the robot dynamics, which needs to be dealt with in application to active SLAM.…”