Asymptotically Optimal Sampling-Based Motion Planning Methods

Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also optimize a cost function, such as path length. Formal path-quality guarantees for continuously valued search spaces are an active area of research interest. Recent results have proven that some sampling-based planning methods probabilistically converge toward the optimal solution as computational effort approaches infinity. This survey summarizes the assumptions behind these popular asymptotically optimal techniques and provides an introduction to the significant ongoing research on this topic.Comment: Posted with permission from the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4. Copyright 2021 by Annual Reviews, https://www.annualreviews.org/. 25 pages. 2 figure

Sampling-Based Motion Planning: A Comparative Review

Sampling-based motion planning is one of the fundamental paradigms to generate robot motions, and a cornerstone of robotics research. This comparative review provides an up-to-date guideline and reference manual for the use of sampling-based motion planning algorithms. This includes a history of motion planning, an overview about the most successful planners, and a discussion on their properties. It is also shown how planners can handle special cases and how extensions of motion planning can be accommodated. To put sampling-based motion planning into a larger context, a discussion of alternative motion generation frameworks is presented which highlights their respective differences to sampling-based motion planning. Finally, a set of sampling-based motion planners are compared on 24 challenging planning problems. This evaluation gives insights into which planners perform well in which situations and where future research would be required. This comparative review thereby provides not only a useful reference manual for researchers in the field, but also a guideline for practitioners to make informed algorithmic decisions.Comment: 25 pages, 7 figures, Accepted for Volume 7 (2024) of the Annual Review of Control, Robotics, and Autonomous System

Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

Reconfiguration of 3D Crystalline Robots Using O(log n) Parallel Moves

We consider the theoretical model of Crystalline robots, which have been introduced and prototyped by the robotics community. These robots consist of independently manipulable unit-square atoms that can extend/contract arms on each side and attach/detach from neighbors. These operations suffice to reconfigure between any two given (connected) shapes. The worst-case number of sequential moves required to transform one connected configuration to another is known to be Theta(n). However, in principle, atoms can all move simultaneously. We develop a parallel algorithm for reconfiguration that runs in only O(log n) parallel steps, although the total number of operations increases slightly to Theta(nlogn). The result is the first (theoretically) almost-instantaneous universally reconfigurable robot built from simple units.Comment: 21 pages, 10 figure

Kinodynamic planning and control of closed-chain robotic systems

Aplicat embargament des de la data de defensa fins el dia 1/6/2022This work proposes a methodology for kinodynamic planning and trajectory control in robots with closed kinematic chains. The ability to plan trajectories is key in a robotic system, as it provides a means to convert high-level task commands¾like “move to that location'', or “throw the object at such a speed''¾into low-level controls to be followed by the actuators. In contrast to purely kinematic planners, which only generate collision-free paths in configuration space, kinodynamic planners compute state-space trajectories that also account for the dynamics and force limits of the robot. In doing so, the resulting motions are more realistic and exploit gravity, inertia, and centripetal forces to the benefit of the task. Existing kinodynamic planners are fairly general and can deal with complex problems, but they require the state coordinates to be independent. Therefore, they are hard to apply to robots with loop-closure constraints whose state space is not globally parameterizable. These constraints define a nonlinear manifold on which the trajectories must be confined, and they appear in many systems, like parallel robots, cooperative arms manipulating an object, or systems that keep multiple contacts with the environment. In this work, we propose three steps to generate optimal trajectories for such systems. In a first step, we determine a trajectory that avoids the collisions with obstacles and satisfies all kinodynamic constraints of the robot, including loop-closure constraints, the equations of motion, or any limits on the velocities or on the motor and constraint forces. This is achieved with a sampling-based planner that constructs local charts of the state space numerically, and with an efficient steering method based on linear quadratic regulators. In a second step, the trajectory is optimized according to a cost function of interest. To this end we introduce two new collocation methods for trajectory optimization. While current methods easily violate the kinematic constraints, those we propose satisfy these constraints along the obtained trajectories. During the execution of a task, however, the trajectory may be affected by unforeseen disturbances or model errors. That is why, in a third step, we propose two trajectory control methods for closed-chain robots. The first method enjoys global stability, but it can only control trajectories that avoid forward singularities. The second method, in contrast, has local stability, but allows these singularities to be traversed robustly. The combination of these three steps expands the range of systems in which motion planning can be successfully applied.Aquest treball proposa una metodologia per a la planificació cinetodinàmica i el control de trajectòries en robots amb cadenes cinemàtiques tancades. La capacitat de planificar trajectòries és clau en un robot, ja que permet traduir instruccions d'alt nivell com ara ¿mou-te cap aquella posició'' o ¿llença l'objecte amb aquesta velocitat'' en senyals de referència que puguin ser seguits pels actuadors. En comparació amb els planificadors purament cinemàtics, que només generen camins lliures de col·lisions a l'espai de configuracions, els planificadors cinetodinàmics obtenen trajectòries a l'espai d'estats que són compatibles amb les restriccions dinàmiques i els límits de força del robot. Els moviments que en resulten són més realistes i aprofiten la gravetat, la inèrcia i les forces centrípetes en benefici de la tasca que es vol realitzar. Els planificadors cinetodinàmics actuals són força generals i poden resoldre problemes complexos, però assumeixen que les coordenades d'estat són independents. Per tant, no es poden aplicar a robots amb restriccions de clausura cinemàtica en els quals l'espai d'estats no admeti una parametrització global. Aquestes restriccions defineixen una varietat diferencial sobre la qual cal mantenir les trajectòries, i apareixen en sistemes com ara els robots paral·lels, els braços que manipulen objectes coordinadament o els sistemes amb extremitats en contacte amb l'entorn. En aquest treball, proposem tres passos per generar trajectòries òptimes per a aquests sistemes. En un primer pas, determinem una trajectòria que evita les col·lisions amb els obstacles i satisfà totes les restriccions cinetodinàmiques, incloses les de clausura cinemàtica, les equacions del moviment o els límits en les velocitats i en les forces d'actuació o d'enllaç. Això s'aconsegueix mitjançant un planificador basat en mostratge aleatori que utilitza cartes locals construïdes numèricament, i amb un mètode eficient de navegació local basat en reguladors quadràtics lineals. En un segon pas, la trajectòria s'optimitza segons una funció de cost donada. A tal efecte, introduïm dos nous mètodes de col·locació per a l'optimització de trajectòries. Mentre els mètodes existents violen fàcilment les restriccions cinemàtiques, els que proposem satisfan aquestes restriccions al llarg de les trajectòries obtingudes. Durant l'execució de la tasca, tanmateix, la trajectòria pot veure's afectada per pertorbacions imprevistes o per errors deguts a incerteses en el model dinàmic. És per això que, en un tercer pas, proposem dos mètodes de control de trajectòries per robots amb cadenes tancades. El primer mètode gaudeix d'estabilitat global, però només permet controlar trajectòries que no travessin singularitats directes del robot. El segon mètode, en canvi, té estabilitat local, però permet travessar aquestes singularitats de manera robusta. La combinació d'aquests tres passos amplia el ventall de sistemes en els quals es pot aplicar amb èxit la planificació cinetodinàmica.Postprint (published version

System Design, Motion Modelling and Planning for a Recon figurable Wheeled Mobile Robot

Over the past ve decades the use of mobile robotic rovers to perform in-situ scienti c investigations on the surfaces of the Moon and Mars has been tremendously in uential in shaping our understanding of these extraterrestrial environments. As robotic missions have evolved there has been a greater desire to explore more unstructured terrain. This has exposed mobility limitations with conventional rover designs such as getting stuck in soft soil or simply not being able to access rugged terrain. Increased mobility and terrain traversability are key requirements when considering designs for next generation planetary rovers. Coupled with these requirements is the need to autonomously navigate unstructured terrain by taking full advantage of increased mobility. To address these issues, a high degree-of-freedom recon gurable platform that is capable of energy intensive legged locomotion in obstacle-rich terrain as well as wheeled locomotion in benign terrain is proposed. The complexities of the planning task that considers the high degree-of-freedom state space of this platform are considerable. A variant of asymptotically optimal sampling-based planners that exploits the presence of dominant sub-spaces within a recon gurable mobile robot's kinematic structure is proposed to increase path quality and ensure platform safety. The contributions of this thesis include: the design and implementation of a highly mobile planetary analogue rover; motion modelling of the platform to enable novel locomotion modes, along with experimental validation of each of these capabilities; the sampling-based HBFMT* planner that hierarchically considers sub-spaces to better guide search of the complete state space; and experimental validation of the planner with the physical platform that demonstrates how the planner exploits the robot's capabilities to uidly transition between various physical geometric con gurations and wheeled/legged locomotion modes

SHARED CONTROL FOR MOBILE ROBOT OBSTACLE AVOIDANCE

The use of robots has become more prevalent in the last several decades in many sectors such as manufacturing, research, and consumer use [18]. With such varying environments and requirements of these robots it has become increasingly important to develop systems capable of adapting and ensuring safety of the robot and surroundings. This study examines shared control as a method of obstacle avoidance for mobile robots. Shared control makes use of multiple control modes to obtain desired properties from each. This lends a wide range of applications of shared control, from assisted wheelchair operation [37] to autonomous vehicle navigation [10]. Shared control allows for highly versatile controllers and enables easier interfacing with humans. In this thesis we propose control strategies for two mobile robots: a kinematic non-holonomic wheeled robot and a dynamic quad-rotor. Lyapunov analysis is used to show stability of the systems while accounting for shared control switching. With the shared control architecture, it is proven the robots always avoid collision with obstacles. The theoretical analysis is validated with experiments which show promising results and motivate shared control as a viable solution for safe navigation in other systems

ArtPlanner: Robust Legged Robot Navigation in the Field

Due to the highly complex environment present during the DARPA Subterranean Challenge, all six funded teams relied on legged robots as part of their robotic team. Their unique locomotion skills of being able to step over obstacles require special considerations for navigation planning. In this work, we present and examine ArtPlanner, the navigation planner used by team CERBERUS during the Finals. It is based on a sampling-based method that determines valid poses with a reachability abstraction and uses learned foothold scores to restrict areas considered safe for stepping. The resulting planning graph is assigned learned motion costs by a neural network trained in simulation to minimize traversal time and limit the risk of failure. Our method achieves real-time performance with a bounded computation time. We present extensive experimental results gathered during the Finals event of the DARPA Subterranean Challenge, where this method contributed to team CERBERUS winning the competition. It powered navigation of four ANYmal quadrupeds for 90 minutes of autonomous operation without a single planning or locomotion failure

On-line 3D path planning for close-proximity surveying with AUVs

We present an approach for planning collision-free paths on-line for an underwater multi-robot system, which is composed by a leading Autonomous Underwater Vehicle (AUV) endowed with a multibeam sonar and high processing capabilities and a second AUV. While the leading AUV follows a safe, pre-planned survey path, the second vehicle, herein referred to as Camera Vehicle (CV), must survey the bottom in close proximity while following the leader, complementing its survey capabilities. Due to their proximity to the bottom, the CV is exposed to a collision threat. We address this problem by incrementally building a 3D map of the environment onboard the leading vehicle by means of its multibeam sonar. Using this map, we plan on-line 3D paths that are transferred to the CV for close and safe surveying of the bottom. These paths are planned using the Transition-based RRT (T-RRT) algorithm, which is an RRT-variant that considers a cost function defined over the vehicle’s configuration space, or costmap for short. By defining a costmap in terms of distance to the bottom and path distance, we are able to keep the paths at a desired offset distance from the bottom for constant-resolution surveying. We have integrated our path planning system with the software architecture of the SPARUS-II and GIRONA500 AUVs. We demonstrate the feasibility of our approach in simulation. The multi-robot system presented is based on the context of the MORPH FP7 EU project

Path Planning Framework for Unmanned Ground Vehicles on Uneven Terrain

In this thesis, I address the problem of long-range path planning on uneven terrain for non-holonomic wheeled mobile robots (WMR). Uneven terrain path planning is essential for search-and-rescue, surveillance, military, humanitarian, agricultural, constructing missions, etc. These missions necessitate the generation of a feasible sequence of waypoints, or reference states, to navigate a WMR from the initial location to the final target location through the uneven terrain. The feasibility of navigating through a given path over uneven terrain can be undermined by various terrain features. Examples of such features are loose soil, vegetation, boulders, steeply sloped terrain, or a combination of all of these elements. I propose a three-stage framework to solve the problem of rapid long-range path planning. In the first stage, RRT-Connect provides a rapid discovery of the feasible solution. Afterward, Informed RRT* improves the feasible solution. Finally, Shortcut heuristics improves the solution locally. To improve the computational speed of path planning algorithms, we developed an accelerated version of the traversability estimation on point clouds based on Principal Component Analysis. The benchmarks demonstrate the efficacy of the path planning approach