Mutual Information for Exploration

Robot exploration is used for applications such as search and rescue. A key bottleneck to exploration speed is the complexity of computing Shannon’s mutual information (MI), which determines the next location that the robot should explore to reduce the uncertainty of an unknown environment ; due to the complexity of MI, roboticists have had to use heuristic-based approaches that do not have provable guarantees. In this project, we develop new algorithms (including Fast computation of Shannon's Mutual Information (FSMI) and Fast Continuous Mutual Information (FCMI)) and hardware architectures for efficient computation of MI, which enable several orders of magnitude speed up allowing for real-time computation for the entire map in a reasonably-sized map (for both 2D and 3D).

ICRA 2020 Paper Video


Zhengdong Zhang, Trevor Henderson, Vivienne Sze, Sertac Karaman, “FSMI: Fast computation of Shannon Mutual Information for information-theoretic mapping,” IEEE International Conference on Robotics and Automation (ICRA), May 2019


Information-based mapping algorithms are crit- ical to robot exploration tasks in several applications rang- ing from disaster response to space exploration. Unfortu- nately, most existing information-based mapping algorithms are plagued by the computational difficulty of evaluating the Shan- non mutual information between potential future sensor mea- surements and the map. This has lead researchers to develop approximate methods, such as Cauchy-Schwarz Quadratic Mutual Information (CSQMI). In this paper, we propose a new algorithm, called Fast Shannon Mutual Information (FSMI), which is significantly faster than existing methods at computing the exact Shannon mutual information. The key insight behind FSMI is recognizing that the integral over the sensor beam can be evaluated analytically, removing an expensive numerical integration. In addition, we provide a number of approximation techniques for FSMI, which significantly improve computation time. Equipped with these approximation techniques, the FSMI algorithm is more than three orders of magnitude faster than the existing computation for Shannon mutual information; it also outperforms the CSQMI algorithm significantly, being roughly twice as fast, in our experiments.

Zhengdong Zhang, Theia Henderson, Sertac Karaman, Vivienne Sze, "FSMI: Fast computation of Shannon Mutual Information for information-theoretic mapping," International Journal of Robotics Research (IJRR), Vol. 39, No. 9, pp. 1155-1177, August 2020


Exploration tasks are embedded in many robotics applications, such as search and rescue and space exploration. Information-based exploration algorithms aim to find the most informative trajectories by maximizing an information- theoretic metric, such as the mutual information between the map and potential future measurements. Unfortunately, most existing information-based exploration algorithms are plagued by the computational difficulty of evaluating the Shannon mutual information metric. In this paper, we consider the fundamental problem of evaluating Shannon mutual information between the map and a range measurement. First, we consider 2D environments. We propose a novel algorithm, called the Fast Shannon Mutual Information (FSMI). The key insight behind the algorithm is that a certain integral can be computed analytically, leading to substantial computational savings. Second, we consider 3D environments, represented by efficient data structures, e.g., an OctoMap, such that the measurements are compressed by Run-Length Encoding (RLE). We propose a novel algorithm, called FSMI-RLE, that efficiently evaluates the Shannon mutual information when the measurements are compressed using RLE. For both the FSMI and the FSMI-RLE, we also propose variants that make different assumptions on the sensor noise distribution for the purpose of further computational savings. We evaluate the proposed algorithms in extensive experiments. In particular, we show that the proposed algorithms outperform existing algorithms that compute Shannon mutual information as well as other algorithms that compute the Cauchy-Schwarz Quadratic mutual information (CSQMI). In addition, we demonstrate the computation of Shannon mutual information on a 3D map for the first time.

Peter Li*, Zhengdong Zhang*, Sertac Karaman, Vivienne Sze, "High-throughput Computation of Shannon Mutual Information on Chip," Robotics: Science and Systems (RSS), June 2019


Exploration problems are fundamental to robotics, arising in various domains, ranging from search and rescue to space exploration. Many effective exploration algorithms rely on the computation of mutual information between the current map and potential future measurements in order to make planning decisions. Unfortunately, computing mutual information metrics is computationally challenging. In fact, a large fraction of the current literature focuses on approximation techniques to devise computationally-efficient algorithms. In this paper, we propose a novel computing hardware architecture to efficiently compute Shannon mutual information. The proposed architecture consists of multiple mutual information computation cores, each evaluating the mutual information between a single sensor beam and the occupancy grid map. The key challenge is to ensure that each core is supplied with data when requested, so that all cores are maximally utilized. Our key contribution consists of a novel memory architecture and data delivery method that ensures effective utilization of all mutual information computation cores. This architecture was optimized for 16 mutual information computation cores, and was implemented on an FPGA. We show that it computes the mutual information metric for an entire map of 20m × 20m at 0.1m resolution in near real time, at 2 frames per second, which is approximately two orders of magnitude faster, while consuming an order of magnitude less power, when compared to an equivalent implementation on a Xeon CPU.

Theia Henderson, Vivienne Sze, Sertac Karaman, “An Efficient and Continuous Approach to Information-Theoretic Exploration,” IEEE International Conference on Robotics and Automation (ICRA), May 2020


Exploration of unknown environments is embed- ded and essential in many robotics applications. Traditional algorithms, that decide where to explore by computing the expected information gain of an incomplete map from future sensor measurements, are limited to very powerful computa- tional platforms. In this paper, we describe a novel approach for computing this expected information gain efficiently, as principally derived via mutual information. The key idea behind the proposed approach is a continuous occupancy map framework and the recursive structure it reveals. This structure makes it possible to compute the expected information gain of sensor measurements across an entire map much faster than computing each measurements’ expected gain independently. Specifically, for an occupancy map composed of |M| cells and a range sensor that emits |Θ| measurement beams, the algorithm (titled FCMI) computes the information gain corresponding to measurements made at each cell in O(|Θ||M|) steps. To the best of our knowledge, this complexity bound is better than all existing methods for computing information gain. In our experiments, we observe that this novel, continuous approach is two orders of magnitude faster than the state-of-the-art FSMI algorithm.

Keshav Gupta, Peter Li, Sertac Karaman, Vivienne Sze, “Efficient Computation of Map-scale Continuous Mutual Information on Chip in Real Time,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), September 2021


Exploration tasks are essential to many emerging robotics applications, ranging from search and rescue to space exploration. The planning problem for exploration requires determining the best locations for future measurements that will enhance the fidelity of the map, for example, by reducing its total entropy. A widely-studied technique involves computing the Mutual Information (MI) between the current map and future measurements, and utilizing this MI metric to decide the locations for future measurements. However, computing MI for reasonably-sized maps is slow and power hungry, which has been a bottleneck towards fast and efficient robotic exploration. In this paper, we introduce a new hardware accelerator architecture for MI computation that features a low-latency, energy-efficient MI compute core and an optimized memory subsystem that provides sufficient bandwidth to keep the cores fully utilized. The core employs interleaving to counter the recursive algorithm, and workload balancing and numerical approximations to reduce latency and energy consumption. We demonstrate this optimized architecture with a Field- Programmable Gate Array (FPGA) implementation, which can compute MI for all cells in an entire 201-by-201 occupancy grid (e.g., representing a 20.1m-by-20.1m map at 0.1m resolution) in 1.55 ms while consuming 1.7 mJ of energy, thus finally rendering MI computation for the whole map real time and at a fraction of the energy cost of traditional compute plat- forms. For comparison, this particular FPGA implementation running on the Xilinx Zynq-7000 platform is two orders of magnitude faster and consumes three orders of magnitude less energy per MI map compute, when compared to a baseline GPU implementation running on an NVIDIA GeForce GTX 980 platform. The improvements are more pronounced when compared to CPU implementations of equivalent algorithms.