Autonomous exploration in mobile robotics often involves a trade-off between two objectives: maximizing environmental coverage and minimizing the total path length. In the widely used information gain paradigm, exploration is guided by the expected value of observations. While this approach is effective under budget-constrained settings--where only a limited number of observations can be made--it fails to align with quality-constrained scenarios, in which the robot must fully explore the environment to a desired level of certainty or quality. In such cases, total information gain is effectively fixed, and maximizing it per step can lead to inefficient, greedy behavior and unnecessary backtracking. This paper argues that information gain should not serve as an optimization objective in quality-constrained exploration. Instead, it should be used to filter viable candidate actions. We propose a novel heuristic, distance advantage, which selects candidate frontiers based on a trade-off between proximity to the robot and remoteness from other frontiers. This heuristic aims to reduce future detours by prioritizing exploration of isolated regions before the robot's opportunity to visit them efficiently has passed. We evaluate our method in simulated environments against classical frontier-based exploration and gain-maximizing approaches. Results show that distance advantage significantly reduces total path length across a variety of environments, both with and without access to prior map predictions. Our findings challenge the assumption that more accurate gain estimation improves performance and offer a more suitable alternative for the quality-constrained exploration paradigm.

Rapidly-exploring Random Tree (RRT) algorithms have been applied successfully to challenging robot motion planning and under-actuated nonlinear control problems. However a fundamental limitation of the RRT approach is the slow convergence in configuration spaces with narrow channels because of the small probability of generating test points inside narrow channels. This paper presents an improved RRT algorithm that takes advantage of narrow channels between the initial and goal states to find shorter paths by improving the exploration of narrow regions in the configuration space. The proposed algorithm detects the presence of narrow channel by checking for collision of neighborhood points with the infeasible set and attempts to add points within narrow channels with a predetermined bias. This approach is compared with the classical RRT and its variants on a variety of benchmark planning problems. Simulation results indicate that the algorithm presented in this paper computes a significantly shorter path in spaces with narrow channels.

Suboptimal search algorithms can often solve much larger problems than optimal search algorithms, and thus have broad practical use. This paper returns to early algorithms like WA*, A*_e and Optimistic search. It studies the commonalities between these approaches in order to build a new bounded-suboptimal algorithm. Combined with recent research on avoiding node re-expansions in bounded-optimal search, a new solution quality bound is developed, which often provides proof of the solution bound much earlier during the search. Put together, these ideas provide a new state-of-the-art in bounded-optimal search.

These instructions are our golden rules that we will always follow, until our algorithm is done running. So, let's get to it! First things first: we need to initialize some things to keep track of some important information as this algorithm runs. We'll create a table to keep track of the shortest known distance to every vertex in our graph. We'll also keep track of the previous vertex that we came from, before we "checked" the vertex that we're looking at currently. Once we have our table all set up, we'll need to give it some values.

We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we perform a chase and escape game on the "landscape" of the cost function. We have created a concrete algorithm for the Traveling Salesman Problem. Our preliminary test indicates a possibility that this new fusion of chases and escapes problem into combinatorial optimization search is fruitful.

Many exponentially-hard problems can be solved by searching through a space of states to determine a sequence of steps constituting a solution. Algorithms that produce optimal solutions (e.g., shortest path) generally require greater computational resources (e.g., time) than their sub-optimal counterparts. Consequently, many optimal algorithms cannot produce any usable solution when the amount of time available is limited or hard to predict in advance. Anytime algorithms address this problem by initially finding a suboptimal solution very quickly and then generating incrementally better solutions with additional time, effectively providing the best solution generated so far anytime it is required. In this research, we generate initial solutions cheaply using a fast search algorithm. We then improve this low-quality solution by identifying subsequences of steps that appear, based on heuristic estimates, to be considerably longer than necessary. Finally, we perform a more expensive search between the endpoints of each subsequence to find a shorter connecting path. We will show that this improves the overall solution incrementally over time while always having a valid solution to return whenever time runs out. We present results that demonstrate in several problem domains that AIRS (Anytime Iterative Refinement of a Solution) rivals other widely used and recognized anytime algorithms and also produces results comparable to other popular (but not anytime) heuristic algorithms such as Bidirectional A* search.

In this paper, we shed light on how powerful congestion control based on local interactions may be obtained. We show how ants can use repellent pheromones and incorporate the effect of crowding to avoid traffic congestion on the optimal path. Based on these interactions, we propose an ant algorithm, the M-unit EigenAnt algorithm, that leads to the selection of the M shortest paths. The ratio of selection of each of these paths is also optimal and regulated by an optimal amount of pheromone on each of them. To the best of our knowledge, the M -unit EigenAnt algorithm is the first antalgorithm that explicitly ensures the selection of the M shortest paths and regulates the amount of pheromone on them such that it is asymptotically optimal. In fact, it is in contrast with most ant algorithms that aim to discover just a single best path. We provide its convergence analysis and show that the steady state distribution of pheromone aligns with the eigenvectors of the cost matrix, and thus is related to its measure of quality. We also provide analysis to show that this property ensues even when the food is moved or path lengths change during foraging. We show that this behavior is robust in the presence of fluctuations and quickly reflects the change in the M optimal solutions. This makes it suitable for not only distributed applications butalso dynamic ones as well. Finally, we provide simulation results for the convergence to the optimal solution under different initial biases, dynamism in lengths of paths, and discovery of new paths.