Real-time path generation, including collision checks, is vital in critical driving scenarios such as navigating non-signalized intersections. These intersections lack organized traffic flow, which raises the risk of accidents. Rapidly Exploring Random Trees (RRT) is a widely adopted algorithm in robotics for motion planning due to its simplicity and probabilistic completeness. Over the years, researchers have made modifications to the basic RRT algorithm to improve its performance in dynamic environments, making it a favored planning algorithm for autonomous driving. Among these variants, probabilistic RRT (pRRT) demonstrates promising capabilities for efficient online replanning. The first part of the thesis thoroughly studies the pRRT algorithm and compares its performance to the standard RRT and RRT* algorithms through Python simulations. The pRRT algorithm outperformed the RRT and RRT* algorithms in terms of success rate and time to find a safe trajectory. The algorithm was implemented experimentally on scaled cars for the validation of its feasibility. The experimental results show good sim-to-real transfer for this algorithm. The second part of the thesis proposes a novel algorithm for path planning. The algorithm outperforms the standard RRT and pRRT techniques in terms of optimality and conformance to human instincts. The generated paths are much smoother and easier for the controller to track. The AV implementation combines the probabilistic RRT with the RRT-Connect algorithm to mitigate the problem of parameter tuning of the standard pRRT algorithm. The idea is to generate intermediate critical points around the obstacles to grow multiple trees between these points, which are then eventually connected if a safe trajectory is found. The algorithm was tested in simulation and showed comparatively better performance in handling obstacles. / Master of Science / Due to uncontrolled traffic flow, non-signalized intersections are critical for autonomous driving. Motion planning is responsible for the vehicle's decision-making and generating actions based on its surroundings. Rapidly Exploring Random Trees (RRT) is one of the most widely used algorithms for motion planning in robotics due to its simplicity and a guarantee of finding a collision-free path if it exists. Due to the randomness of the algorithm, the time to find a collision-free path increases rapidly as the surrounding environment complicates. In this thesis, we thoroughly study a modified version of RRT called the probabilistic RRT (pRRT) for motion planning of autonomous vehicles. The pRRT algorithm reduces the randomness of the standard RRT algorithm and takes into account the destination location and the positions of the obstacles to find a path around the obstacles and toward the destination point. The algorithm was experimentally validated and confirmed the simplistic transfer from simulations to reality. In the second part of the thesis, we propose a novel algorithm that combines the properties of pRRT and another well-known algorithm called RRT-Connect. This algorithm plans collision-free paths from the start, and the goal points towards free space around the obstacles simultaneously and then combines these fragmented paths. This reduces the overall planning time and was found to be better at providing smooth paths.

Control of complex systems satisfying rich temporal specification has become an increasingly important research area in fields such as robotics, control, automotive, and manufacturing. Popular specification languages include temporal logics, such as Linear Temporal Logic (LTL) and Computational Tree Logic (CTL), which extend propositional logic to capture the temporal sequencing of system properties. The focus of this dissertation is on the control of high-dimensional systems and on timed specifications that impose explicit time bounds on the satisfaction of tasks. This work proposes and evaluates methods and algorithms for synthesizing provably correct control policies that deal with the scalability problems. Ideas and tools from formal verification, graph theory, and incremental computing are used to synthesize satisfying control strategies. Finite abstractions of the systems are generated, and then composed with automata encoding the specifications. The first part of this dissertation introduces a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The specification has two parts: (1) a global specification given as an LTL formula over a set of static service requests that occur at the regions of a known environment, and (2) a local specification that requires servicing a set of dynamic requests that can be sensed locally during the execution. The proposed computational framework consists of two main ingredients: (a) an off-line sampling-based algorithm for the construction of a global transition system that contains a path satisfying the LTL formula, and (b) an on-line sampling-based algorithm to generate paths that service the local requests, while making sure that the satisfaction of the global specification is not affected. The second part of the dissertation focuses on stochastic systems with temporal and uncertainty constraints. A specification language called Gaussian Distribution Temporal Logic is introduced as an extension of Boolean logic that incorporates temporal evolution and noise mitigation directly into the task specifications. A sampling-based algorithm to synthesize control policies is presented that generates a transition system in the belief space and uses local feedback controllers to break the curse of history associated with belief space planning. Switching control policies are then computed using a product Markov Decision Process between the transition system and the Rabin automaton encoding the specification.The approach is evaluated in experiments using a camera network and ground robot. The third part of this dissertation focuses on control of multi-vehicle systems with timed specifications and charging constraints. A rich expressivity language called Time Window Temporal Logic (TWTL) that describes time bounded specifications is introduced. The temporal relaxation of TWTL formulae with respect to the deadlines of tasks is also discussed. The key ingredient of the solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the given formula. The annotated automata are composed with transition systems encoding the motion of all vehicles, and with charging models to produce control strategies for all vehicles such that the overall system satisfies the mission specification. The methods are evaluated in simulation and experimental trials with quadrotors and charging stations.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In order to navigate dynamic, cluttered environments safely, fully autonomous Unmanned Aerial Vehicles (UAVs) are required to plan conflict-free trajectories between two states in position-time space efficiently and reliably. Kinodynamic planning for vehicles with non-holonomic dynamic constraints is an NP-hard problem which is usually addressed using sampling-based, probabilistically complete motion planning algorithms. These algorithms are often applied in conjunction with a finite set of simple geometric motion primitives which encapsulate the dynamic constraints of the vehicle. This ensures that composite trajectories generated by the planning algorithm adhere to the vehicle dynamics. For many vehicles, accurate tracking of position-based trajectories is a non-trivial problem which demands complicated control techniques with high energy requirements. In an effort to reduce control complexity and thus also energy consumption, a generic Local Planning Method (LPM), able to plan trajectories based on implicitly-defined motion primitives, is developed in this project. This allows the planning algorithm to construct trajectories which are based on simulated results of vehicle motion under the control of a rudimentary auto-pilot, as opposed to a more complicated position-tracking system. The LPM abstracts motion primitives in such a way that it may theoretically be made applicable to various vehicles and control systems through simple substitution of the motion primitive set. The LPM, which is based on a variation of the Levenberg-Marquardt Algorithm (LMA), is integrated into a well-known Probabilistic Roadmap (PRM) kinodynamic planning algorithm which is known to work well in dynamic and cluttered environments. The complete motion planning algorithm is tested thoroughly in various simulated environments, using a vehicle model and controllers which have been previously verified against a real UAV during practical flight tests. / AFRIKAANSE OPSOMMING: Ten einde dinamiese, voorwerpryke omgewings veilig te navigeer, word daar vereis dat volledig-outonome onbemande lugvoertuie konflikvrye trajekte tussen twee posisie-tydtoestande doeltreffend en betroubaar kan beplan. Kinodinamiese beplanning is ’n NPmoeilike probleem wat gewoonlik deur middel van probabilisties-volledige beplanningsalgoritmes aangespreek word . Hierdie algoritmes word dikwels in kombinasie met ’n eindige stel eenvoudige geometriese maneuvers, wat die dinamiese beperkings van die voertuig omvat, ingespan. Sodanig word daar verseker dat trajekte wat deur die beplaningsalgoritme saamgestel is aan die dinamiese beperkings van die voertuig voldoen. Vir baie voertuie, is die akkurate volging van posisie-gebaseerde trajekte ’n nie-triviale probleem wat die gebruik van ingewikkelde, energie-intensiewe beheertegnieke vereis. In ’n poging om beheer-kompleksiteit, en dus energie-verbruik, te verminder, word ’n generiese plaaslike-beplanner voorgestel. Hierdie algoritme stel die groter kinodinamiese beplanner in staat daartoe om trajekte saam te stel wat op empiriese waarnemings van voertuig-trajekte gebaseer is. ’n Eenvoudige beheerstelsel kan dus gebruik word, in teenstelling met die meer ingewikkelde padvolgingsbeheerders wat benodig word om eenvoudige geometriese trajekte akkuraat te volg. Die plaaslike-beplanner abstraeer maneuvers in so ’n mate dat dit teoreties op verskeie voertuie en beheerstelsels van toepassing gemaak kan word deur eenvoudig die maneuver-stel te vervang. Die plaaslike-beplanner, wat afgelei is van die Levenberg-Marquardt-Algoritme (LMA), word in ’n welbekende “Probabilistic Roadmap” (PRM) kinodinamiese-beplanningsalgoritme geïntegreer. Dit word algemeen aanvaar dat die PRM effektief werk in dinamiese, voorwerpryke omgewings. Die volledige beplanningsalgoritme word deeglik in verskeie, gesimuleerde omgewings getoets op ’n voertuig-model en -beheerders wat voorheen vir akkuraatheid teenoor ’n werklike voertuig gekontroleer is tydens praktiese vlugtoetse.

La conception de protéines ayant des propriétés spécifiques représente un enjeu majeur pour la pharmacologie et les bio-technologies. Malgré les progrès des méthodes de CAO développées pour la conception de protéines, une limitation majeure des techniques existantes vient de la difficulté à prendre en compte la mobilité du squelette protéique, afin de mieux capturer l’ensemble des propriétés des protéines candidates et garantir la bonne stabilité de la protéine choisie dans la conformation voulue. De plus, si des méthodes de conception multi-états ont été proposées, elles ne permettent pas de garantir l’existence d’une trajectoire réaliste entre ces états. De ce fait, la conception de protéines devant permettre la transition entre plusieurs états reste un problème hors de la portée des méthodes actuelles. Cette thèse explore comment des algorithmes inspirés de la robotique peuvent être utilisés pour explorer l’espace conformationnel de manière efficace afin d’améliorer les méthodes de conception de protéines en prenant en compte de manière plus poussée la flexibilité de leur squelette. Ce travail pose également un premier jalon vers une méthode de conception adaptée à la réalisation d’un mouvement de la protéine. / The ability to design proteins with specific properties would yield great progress in pharmacology and bio-technologies. Methods to design proteins have been developed since a few decades and some relevant achievements have been made including de novo protein design. Yet, current approaches suffer some serious limitations. By not taking protein’s backbone motions into account, they fail at capturing some of the properties of the candidate design and cannot guarantee that the solution will in fact be stable for the goal conformation. Besides, although multi-states design methods have been proposed, they do not guarantee that a feasible trajectory between those states exists, which means that design problem involving state transitions are out of reach of the current methods. This thesis investigates how robotics-inspired algorithms can be used to efficiently explore the conformational landscape of a protein aiming to enhance protein design methods by introducing additional backbone flexibility. This work also provides first milestones towards protein motion design.

Robot motion planning is one of the central problems in robotics, and has received considerable amount of attention not only from roboticists but also from the control and artificial intelligence (AI) communities. Despite the different types of applications and physical properties of robotic systems, many high-level tasks of autonomous systems can be decomposed into subtasks which require point-to-point navigation while avoiding infeasible regions due to the obstacles in the workspace. This dissertation aims at developing a new class of sampling-based motion planning algorithms that are fast, efficient and asymptotically optimal by employing ideas from Machine Learning (ML) and Dynamic Programming (DP). First, we interpret the robot motion planning problem as a form of a machine learning problem since the underlying search space is not known a priori, and utilize random geometric graphs to compute consistent discretizations of the underlying continuous search space. Then, we integrate existing DP algorithms and ML algorithms to the framework of sampling-based algorithms for better exploitation and exploration, respectively. We introduce a novel sampling-based algorithm, called RRT#, that improves upon the well-known RRT* algorithm by leveraging value and policy iteration methods as new information is collected. The proposed algorithms yield provable guarantees on correctness, completeness and asymptotic optimality. We also develop an adaptive sampling strategy by considering exploration as a classification (or regression) problem, and use online machine learning algorithms to learn the relevant region of a query, i.e., the region that contains the optimal solution, without significant computational overhead. We then extend the application of sampling-based algorithms to a class of stochastic optimal control problems and problems with differential constraints. Specifically, we introduce the Path Integral - RRT algorithm, for solving optimal control of stochastic systems and the CL-RRT# algorithm that uses closed-loop prediction for trajectory generation for differential systems. One of the key benefits of CL-RRT# is that for many systems, given a low-level tracking controller, it is easier to handle differential constraints, so complex steering procedures are not needed, unlike most existing kinodynamic sampling-based algorithms. Implementation results of sampling-based planners for route planning of a full-scale autonomous helicopter under the Autonomous Aerial Cargo/Utility System Program (AACUS) program are provided.

This paper deals with the problem of object path planning in 3D space. The goal is to create program which allows users to create a scene used for path planning, perform the planning and finally visualize path in the scene. Work is focused on probabilistic algorithms that are described in the theoretical part. The practical part describes the design and implementation of application. Finally, several experiments are performed to compare the performance of different algorithms and demonstrate the functionality of the program.