A scalable method for parallelizing sampling-based motion planning algorithms

Abstract—This paper describes a scalable method for paral-lelizing sampling-based motion planning algorithms. It subdi-vides configuration space (C-space) into (possibly overlapping) regions and independently, in parallel, uses standard (sequen-tial) sampling-based planners to construct roadmaps in each region. Next, in parallel, regional roadmaps in adjacent regions are connected to form a global roadmap. By subdividing the space and restricting the locality of connection attempts, we reduce the work and inter-processor communication associated with nearest neighbor calculation, a critical bottleneck for scalability in existing parallel motion planning methods. We show that our method is general enough to handle a variety of planning schemes, including the widely used Probabilistic Roadmap (PRM) and Rapidly-exploring Random Trees (RRT) algorithms. We compare our approach to two other existing parallel algorithms and demonstrate that our approach achieves better and more scalable performance. Our approach achieves almost linear scalability on a 2400 core LINUX cluster and on a 153,216 core Cray XE6 petascale machine. I

Sampling-based Algorithms for Optimal Motion Planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics Researc

TOGGLE PRM: A SIMULTANEOUS MAPPING OF CFREE AND COBSTACLE FOR USE IN PROBABILISTIC ROADMAP METHODS

Motion planning for robotic applications is difficult. This is a widely studied problem in which the best known deterministic solution is doubly exponential in the dimensionality of the problem. A class of probabilistic planners, called sampling-based planners, have shown much success in this area, but still show weakness for planning in difficult parts of the space, namely narrow passages. The problem space is made of two subsets - free space and collision space, representing valid and invalid robot positions. A general method for probabilistic planners is the probabilistic roadmap method (PRM) which maps only free space to find a solution. This thesis proposes a new strategy, Toggle PRM, for probabilistic roadmap planners, which simultaneously maps both free space and collision space in order to guide the solution more efficiently. All sampled robotic configurations are kept in two separate maps. When the connection attempts between configurations in one roadmap fail, the witness to the failure is retained as a configuration in the opposing roadmap. By mapping both spaces, sampling density in narrow passages is greatly increased. A theoretical and experimental analysis of Toggle PRM shows the independence from the volume of a narrow passage and the volume of the obstacles surrounding the passage for sampling, overcoming a previous challenge of probabilistic planning. Additionally, Toggle PRM has increased efficiency as compared to other common sampling techniques in various motion planning problems because of this improved sampling in narrow passages

REACTIVE MOTION REPLANNING FOR HUMAN-ROBOT COLLABORATION

Negli ultimi anni si è assistito a un incremento significativo di robot che condividono lo spazio di lavoro con operatori umani, per combinare la rapidità e la precisione proprie dei robot con l'adattabilità e l'intelligenza umana. Tuttavia, questa integrazione ha introdotto nuove sfide in termini di sicurezza ed efficienza della collaborazione. I robot devono essere in grado di adattarsi prontamente ai cambiamenti nell'ambiente circostante, come i movimenti degli operatori, adeguando in tempo reale il loro percorso per evitare collisioni, preferibilmente senza interruzioni. Inoltre, nelle operazioni di collaborazione tra uomo e robot, le traiettorie ripianificate devono rispettare i protocolli di sicurezza, al fine di evitare rallentamenti e fermate dovute alla prossimità eccessiva del robot all'operatore. In questo contesto è fondamentale fornire soluzioni di alta qualità in tempi rapidi per garantire la reattività del robot. Le tecniche di ripianificazione tradizionali tendono a faticare in ambienti complessi, soprattutto quando si tratta di robot con molti gradi di libertà e numerosi ostacoli di dimensioni considerevoli. La presente tesi affronta queste sfide proponendo un nuovo algoritmo sampling-based di ripianificazione del percorso per manipolatori robotici. Questo approccio sfrutta percorsi pre-calcolati per generare rapidamente nuove soluzioni in poche centinaia di millisecondi. Inoltre, incorpora una funzione di costo che guida l'algoritmo verso soluzioni che rispettano lo standard di sicurezza ISO/TS 15066, riducendo così gli interventi di sicurezza e promuovendo una cooperazione efficiente tra uomo e robot. Viene inoltre presentata un'architettura per gestire il processo di ripianificazione durante l'esecuzione del percorso del robot. Infine, viene introdotto uno strumento software che semplifica l'implementazione e il testing degli algoritmi di ripianificazione del percorso. Simulazioni ed esperimenti condotti su robot reali dimostrano le prestazioni superiori del metodo proposto rispetto ad altre tecniche popolari.In recent years, there has been a significant increase in robots sharing workspace with human operators, combining the speed and precision inherent to robots with human adaptability and intelligence. However, this integration has introduced new challenges in terms of safety and collaborative efficiency. Robots now need to swiftly adjust to dynamic changes in their environment, such as the movements of operators, altering their path in real-time to avoid collisions, ideally without any disruptions. Moreover, in human-robot collaborations, replanned trajectories should adhere to safety protocols, preventing safety-induced slowdowns or stops caused by the robot's proximity to the operator. In this context, quickly providing high-quality solutions is crucial for ensuring the robot's responsiveness. Conventional replanning techniques often fall short in complex environments, especially for robots with numerous degrees of freedom contending with sizable obstacles. This thesis tackles these challenges by introducing a novel sampling-based path replanning algorithm tailored for robotic manipulators. This approach exploits pre-computed paths to generate new solutions in a few hundred milliseconds. Additionally, it integrates a cost function that steers the algorithm towards solutions that strictly adhere to the ISO/TS 15066 safety standard, thereby minimizing the need for safety interventions and fostering efficient cooperation between humans and robots. Furthermore, an architecture for managing the replanning process during the execution of the robot's path is introduced. Finally, a software tool is presented to streamline the implementation and testing of path replanning algorithms. Simulations and experiments conducted on real robots demonstrate the superior performance of the proposed method compared to other popular techniques

Metrics for sampling-based motion planning

A motion planner finds a sequence of potential motions for a robot to transit from an initial to a goal state. To deal with the intractability of this problem, a class of methods known as sampling-based planners build approximate representations of potential motions through random sampling. This selective random exploration of the space has produced many remarkable results, including solving many previously unsolved problems. Sampling-based planners usually represent the motions as a graph (e.g., the Probabilistic Roadmap Methods or PRMs), or as a tree (e.g., the Rapidly exploring Random Tree or RRT). Although many sampling-based planners have been proposed, we do not know how to select among them because their different sampling biases make their performance depend on the features of the planning space. Moreover, since a single problem can contain regions with vastly different features, there may not exist a simple exploration strategy that will perform well in every region. Unfortunately, we lack quantitative tools to analyze problem features and planners performance that would enable us to match planners to problems. We introduce novel metrics for the analysis of problem features and planner performance at multiple levels: node level, global level, and region level. At the node level, we evaluate how new samples improve coverage and connectivity of the evolving model. At the global level, we evaluate how new samples improve the structure of the model. At the region level, we identify groups or regions that share similar features. This is a set of general metrics that can be applied in both graph-based and tree-based planners. We show several applications for these tools to compare planners, to decide whether to stop planning or to switch strategies, and to adjust sampling in different regions of the problem

Knowledge-oriented task and motion planning for multiple mobile robots

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of experimental and theoretical artificial intelligence, published online: 30 Nov 2018 available online: https://www.tandfonline.com/doi/abs/10.1080/0952813X.2018.1544280Robotic systems composed of several mobile robots moving in human environments pose several problems at perception, planning and control levels. In these environments, there may be obstacles obstructing the paths, which robots can remove by pushing or pulling them. At planning level, therefore, an efficient combination of task and motion planning is required. Even more if we assume a cooperative system in which robots can collaborate with each other by e.g. pushing together a heavy obstacle or by one robot clearing the way to another one. In this paper, we cope with this problem by proposing ¿-TMP, a smart combination of an heuristic task planner based on the Fast Forward method, a physics-based motion planner, and reasoning processes over the ontologies that code the knowledge on the problem. The significance of the proposal relies on how geometric and physics information is used within the computation of the heuristics in order to guide the symbolic search, i.e. how an artificial intelligence planning method is combined with low-level motion planning to achieve a feasible sequence of actions (composed of collision-free motions plus physically-feasible push/pull actions). The proposal has been validated with several simulated scenarios (using up to five robots that need to collaborate with each other to reach the goal state), showing how the method is able to solve challenging situations and also find an efficient solution in terms of power.Peer ReviewedPostprint (author's final draft

Tools for User Modification of Optimal Roadmaps

Robotic motion planning is a ubiquitous field of study, with innumerable applications in sci- ence, engineering, and beyond. At its core, however, motion planning is infeasible for many complex problems. Sampling-based algorithms address this issue by building an approximate model of the planning space, while optimal planners extend this to provide desirable guaran- tees on solution features (e.g., shortest paths). Unfortunately, these guarantees can require the creation of dense, cumbersome planning graphs. Automatic refinement algorithms can help to sparsify these dense graphs, though they may be costly themselves if they affect the quality of the original solution. In another direction, harnessing human intuition with user- guided planning strategies has also shown promise. In this research, we seek to combine the unique strengths of human and machine reasoning with a foundational, interactive toolset for graph modification and, thus, to overcome some weaknesses inherent in either alone. We provide a visual interface that allows the user to modify a pre-computed planning graph by adding, removing, and adjusting vertices and edges as desired, with reciprocal feedback from the planner on the feasibility of each operation. This provides a more adaptable way to improve graph quality–e.g., by sparsifying particular areas based on the unique dynamics of the environment, which are easily and naturally conceptualized by human instinct. In experiments, we found our tools to be quite helpful in improving some measures of graph quality, while their benefits on others dependended on the intuitiveness of the user interface