Efficient motion planning for problems lacking optimal substructure

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra's algorithm. Our algorithm runs in $O\left((n_B\cdot n) \log( n_B\cdot n) + n_B\cdot m\right)$ time, where~$n$ and $m$ are the number of vertices and edges of the graph, respectively, and $n_B$ is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm

Toward Asymptotically-Optimal Inspection Planning via Efficient Near-Optimal Graph Search

Inspection planning, the task of planning motions that allow a robot to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans that inspect the points of interest grows exponentially with the number of inspected points. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion planning roadmap using sampling-based algorithms, and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We demonstrate IRIS's efficacy on a simulated planar 5DOF manipulator inspection task and on a medical endoscopic inspection task for a continuum parallel surgical robot in anatomy segmented from patient CT data. We show that IRIS computes higher-quality inspection paths orders of magnitudes faster than a prior state-of-the-art method.Comment: RSS 201

Optimal hyperpaths with non-additive link costs

Non-additive link cost functions are common and important for a range of assignment problems. In particular in transit assignment, but also a range of other problems path splits further need to consider node cost uncertainties leading to the notion of hyperpaths. We discuss the problem of finding optimal hyperpaths under non-additive link cost conditions assuming a cost vector with a limited number of marginal decreasing costs depending on the number of links already traversed. We illustrate that these non-additive costs lead to violation of Bellman’s optimality principle which in turn means that standard procedures to obtain optimal destination specific hyperpath trees are not feasible. To overcome the problem we introduce the concepts of a “travel history vector” and active critical, passive critical and fixed nodes. The former records the expected number of traversed links until a node, and the latter distinguishes nodes for which the cost can be determined deterministically. With this we develop a 2-stage solution approach. In the first stage we test whether the optimal hyperpath can be obtained by backward search. If this is not the case, we propose a so called “selective hyperpath generation” among hyperpaths to a (small) number of active critical nodes and combine this with standard hyperpath search. We illustrate our approach by applying it to the Sioux Falls network showing that even for link cost functions with large step changes we are able to obtain optimal hyperpaths in a reasonable computational time

The Multiobjective Average Network Flow Problem: Formulations, Algorithms, Heuristics, and Complexity

Integrating value focused thinking with the shortest path problem results in a unique formulation called the multiobjective average shortest path problem. We prove this is NP-complete for general graphs. For directed acyclic graphs, an efficient algorithm and even faster heuristic are proposed. While the worst case error of the heuristic is proven unbounded, its average performance on random graphs is within 3% of the optimal solution. Additionally, a special case of the more general biobjective average shortest path problem is given, allowing tradeoffs between decreases in arc set cardinality and increases in multiobjective value; the algorithm to solve the average shortest path problem provides all the information needed to solve this more difficult biobjective problem. These concepts are then extended to the minimum cost flow problem creating a new formulation we name the multiobjective average minimum cost flow. This problem is proven NP-complete as well. For directed acyclic graphs, two efficient heuristics are developed, and although we prove the error of any successive average shortest path heuristic is in theory unbounded, they both perform very well on random graphs. Furthermore, we define a general biobjective average minimum cost flow problem. The information from the heuristics can be used to estimate the efficient frontier in a special case of this problem trading off total flow and multiobjective value. Finally, several variants of these two problems are discussed. Proofs are conjectured showing the conditions under which the problems are solvable in polynomial time and when they remain NP-complete

Calcul d'itinéraire multimodal et multiobjectif en milieu urbain

With the growth of environmental awareness and high energy prices, more and more people use public transport, cycle or walk. However, just one mean of transport cannot cover all the transportation needs. Therefor, combining different means of transport is often an interesting solution. Finding the best multimodal route for a given person is a hard task. Every person has different opinions concerning the duration, the cost, pollution, number of changes etc. Even the same person might choose different paths depending on circumstances: if it's raining he will not cycle and if he has to carry heavy luggages, he will avoid changes. Multicriteria optimization allows to suggest multiple solutions that are said to be equivalent. The user will chose the route that fits the best according to his preferences at a given moment. The main problem to solve is the shortest multimodal time dependent path. The challenge is to have results in less than a second on a large city in order to have a real life application. A great care has been taken to remain simple an generic. We do not restrict the number of means of transport nor the considered objectives. We adapted algorithms known for their theoretical or experimental performances in order to take in account the time dependency or to be multiobjective. Well also suggest heuristics to keep computation time around one second. The algorithms have been tested with success on San Francisco, Los Angeles and Rennes.Par conscience environnementale ou à cause des coûts de l'énergie, de plus en plus de personnes utilisent les transports en commun ou les transports doux. Cependant, un seul mode de transport ne peut pas couvrir tous les besoins. De ce fait, la combinaison de différents modes de transport est une solution très intéressante. Trouver le meilleur chemin multimodal pour une personne donnée est une tâche difficile. Chaque personne a des préférences différentes concernant la durée, le coût, la pollution, les changements, etc. De plus, le choix d'un même usager dépendent des circonstances. S'il pleut, il ne prendra pas le vélo et s'il a des bagages encombrants, il évitera les changements. L'optimisation multiobjectif permet de proposer plusieurs solutions dites équivalentes. Ainsi l'utilisateur choisira l'itinéraire qui lui convient en fonction de ses préférences à un moment donné. Le problème principal à résoudre est donc celui du plus court chemin multiobjectif de point à point dépendant du temps. L'enjeu est d'être capable d'avoir des résultats de l'ordre de la seconde pour une grande ville pour envisager une application réelle. Une attention particulière a été portée sur la simplicité et la généricité des approches proposées. Nous ne nous restreignons pas à un nombre prédéfini de modes de transport ou d'objectifs. Plusieurs algorithmes réputés pour leurs performances théoriques ou expérimentales ont été adaptés au cas multiobjectif ou à la dépendance du temps. Nous avons également proposé des heuristiques permettant de garder le temps de calcul de l'ordre de la seconde

Energy-Efficient Technologies for High-Performance Manufacturing Industries

Ph.DDOCTOR OF PHILOSOPH

Efficient Motion and Inspection Planning for Medical Robots with Theoretical Guarantees

Medical robots enable faster and safer patient care. Continuum medical robots (e.g., steerable needles) have great potential to accomplish procedures with less damage to patients compared to conventional instruments (e.g., reducing puncturing and cutting of tissues). Due to their complexity and degrees of freedom, such robots are often harder and less intuitive for physicians to operate directly. Automating robot-assisted medical procedures can enable physicians and patients to harness the full potential of medical robots in terms of safety, efficiency, accuracy, and precision.Motion planning methods compute motions for a robot that satisfy various constraints and accomplish a specific task, e.g., plan motions for a mobile robot to move to a target spot while avoiding obstacles. Inspection planning is the task of planning motions for a robot to inspect a set of points of interest, and it has applications in domains such as industrial, field, and medical robotics. With motion and inspection planning, medical robots would be able to automatically accomplish tasks like biopsy and endoscopy while minimizing safety risks and damage to the patient. Computing a motion or inspection plan can be computationally hard since we have to consider application-specific constraints, which come from the robotic system due to the mechanical properties of the robot or come from the environment, such as the requirement to avoid critical anatomical structures during the procedure.I develop motion and inspection planning algorithms that focus on efficiency and effectiveness. Given the same computing power, higher efficiency would shorten the procedure time, thus reducing costs and improving patient outcomes. Additionally, for the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the algorithms involved in procedure automation. Therefore, I focus on providing theoretical guarantees to certify the performance of planners. More specifically, it is important to certify if a planner is able to find a plan if one exists (i.e., completeness) and if a planner is able to find a globally optimal plan according to a given metric (i.e., optimality).Doctor of Philosoph