Complete Path Planning for a Tetris-Inspired Self-Reconfigurable Robot by the Genetic Algorithm of the Traveling Salesman Problem

Abstract

The efficiency of autonomous systems that tackle tasks such as home cleaning, agriculture harvesting, and mineral mining depends heavily on the adopted area coverage strategy. Extensive navigation strategies have been studied and developed, but few focus on scenarios with reconfigurable robot agents. This paper proposes a navigation strategy that accomplishes complete path planning for a Tetris-inspired hinge-based self-reconfigurable robot (hTetro), which consists of two main phases. In the first phase, polyomino form-based tilesets are generated to cover the predefined area based on the tiling theory, which generates a series of unsequenced waypoints that guarantee complete coverage of the entire workspace. Each waypoint specifies the position of the robot and the robot morphology on the map. In the second phase, an energy consumption evaluation model is constructed in order to determine a valid strategy to generate the sequence of the waypoints. The cost value between waypoints is formulated under the consideration of the hTetro robot platform’s kinematic design, where we calculate the minimum sum of displacement of the four blocks in the hTetro robot. With the cost function determined, the waypoint sequencing problem is then formulated as a travelling salesman problem (TSP). In this paper, a genetic algorithm (GA) is proposed as a strong candidate to solve the TSP. The GA produces a viable navigation sequence for the hTetro robot to follow and to accomplish complete coverage tasks. We performed an analysis across several complete coverage algorithms including zigzag, spiral, and greedy search to demonstrate that TSP with GA is a valid and considerably consistent waypoint sequencing strategy that can be implemented in real-world hTetro robot navigations. The scalability of the proposed framework allows the algorithm to produce reliable results while navigating within larger workspaces in the real world, and the flexibility of the framework ensures easy implementation of the algorithm on other polynomial-based shape shifting robots.

Realization Energy Optimization of Complete Path Planning in Differential Drive Based Self-Reconfigurable Floor Cleaning Robot

“…In this paper, due to the introduction of hTetro tiling theory and the generated tileset, complete coverage of the entire workspace is guaranteed; therefore, the algorithms implemented to solve the path planning problem focus on the minimization of hTetro power consumption. The two evolutionary algorithms implemented, GA and ACO, are being compared with precedented algorithms such as zigzag, spiral, greedy search, and algorithms introduced in the work of [22], which are all valid approaches to solve TSP-based problems. It is worth noting that algorithms such as zigzag patterned motion are currently the most prominent algorithm that has been implemented in mobile floor cleaning robots.…”

“…Concerning the associated cost weights, the proposed methods can generate the optimal trajectory with the lowest value. In comparison with the method [22], despite yielding the navigation sequence with longer Euclidean distance, the found navigation sequence of the proposed method is different, and its total cost weight calculated by Equation (9) which reflects actual actions during navigation to connect waypoints of hTetro is considerably lower. Typically in Figure 14a with the trajectory sequence of GA and ACO as 1, 3, 2, 7, 9, 6, 4, 5, 8, we can realize these algorithms choice the navigation sequence to connect 2 waypoints with the same morphology first (waypoint 1 to waypoint 3 with the same O shape) instead of link the point at the nearest location (waypoint 1 with O and waypoint 2 with J shape).…”

“…The total associated cost calculated by Equation (9) and navigation sequence for each workspace is showed in Figure 13. Table 5 presents the associated cost weights and execution time of several tested CCPP methods including zigzag scanning, spiral scanning, the greedy search, method [22] and the proposed method with GA and ACO for 11 × 11 workspace including 28 waypoints. To conduct the fair comparison, the Table 5 includes both the total cost weight calculated by the total Euclidean distance between waypoint locations which can be considered that only translation action is involved during hTetro navigation and the cost for all three actions transformation, orientation correction and translation calculated by proposed cost function as Equation (9).…”

“…The greedy search optimal trajectories from the starting waypoint to the next nearest waypoint with the lowest associated cost to link all the waypoints. In our previous work [22], the waypoint sequencing problem is formulated as TSP in which the cost value spending to navigate between two waypoints is being formulated under consideration the minimum sum of displacement of the four hTetro robot blocks. As one can observe, the running time of the methods-based TSP is slightly higher than zigzag and spiral methods and considerably lower than the greedy search.…”

“…Due to the complexity of the actions that could be performed in reconfigurable robots and the interactions between different robot reconfigurations and the workspace obstacles, conventional CCPP algorithms are no longer suitable to be implemented directly on reconfigurable cleaning robot platforms. Based on the platform of the hTetro robot, Le et al, proposed a CCPP algorithm using waypoints generated by the polyomino tiling theory and attempted to find the optimal path while formulating the CCPP problem as a Travelling Salesman Problem (TSP) [22], which put a strong focus on the search for a route with the lowest cost that connect all the waypoints within the workspace to ensure complete area coverage. In the paper, the cost function was defined based on the shortest distance that connects each waypoint; however, due to the introduction of reconfigurability to the robot, the cost function should be modeled so that it takes the cost of robot reconfiguration and rotation into consideration to produce more accurate results.…”