Robot Motion Planning

A significant growth of interest in the pursuit of autonomous vehicles from various stakeholders has been witnessed recently. This indicates that future transportation systems will be autonomous. By the nature of the transportation problem, a transportation system is favourable if it is fast, safe and reliable. Therefore, if autonomous vehicles are to offer a genuinely superior alternative to present-day transportation systems, it is imperative that they do better than present-day transport in all these criteria. This thesis focusses on two submodules of a typical autonomous navigation system that play a critical role in the fulfilment of these criteria. These submodules are path planning and path tracking. Path planning generates safe and optimal paths that result in reaching destinations safely and in minimal time. A path planner should also generate a plan quickly, otherwise delays are incurred. Path tracking is concerned with the accurate following of planned paths so that no collisions result. For a path tracker to accurately follow a planned path, it is necessary that the path be feasible for the target vehicle, otherwise both the path-planning and path-tracking efforts are in vain, as the vehicle will certainly deviate from the path and run the risk of collision. Path-planning algorithms exist that plan paths quickly and efficiently. Such path planners have, however, been proven to be almost-surely suboptimal. At the other end of the spectrum, path-planning algorithms exist that are guaranteed to find optimal paths. However, their optimality guarantee hinges on the number of planning iterations approaching infinity -in technical terms they are said to be asymptotically optimal, with the practical implication being that they may run for unbearably long periods. This thesis investigates the application of path optimisation to accelerate the rate of convergence of path-planning algorithms towards the optimal solution. The thesis first selects and develops suitable path-planning and path-optimisation algorithms to be used for the investigation. To ensure that the paths generated can be accurately executed by targeted vehicles, the developed path planners and path optimisers are adapted to incorporate motion constraints. The path optimisers are then incorporated into the various path planners with the aim of accelerating the rate of convergence and the effectiveness of each path optimiser in accelerating the convergence of each path planner is analysed. Of interest in this investigation is to ascertain if the application of path optimisation to accelerate the rate of convergence of the path planners helps a quick and efficient, though almost-surely suboptimal, path planner attain comparable or better performance than that of an asymptotically optimal path planner. Results obtained from the experiments indicate the affirmative. Without demonstrating that the planned paths are indeed executable, the practical value of the developed optimised path-planning algorithms would be unclear. A path tracker has therefore been developed that accurately tracks planned paths in the absence of disturbances, and is able to correct for deviations when disturbances are encountered. ii Stellenbosch University "It always seems impossible until it is done." -Nelson Rolihlahla Mandela. This research has been the biggest, most challenging, and yet most rewarding adventure in my life thus far. Looking back, I have no regrets for leaving gainful employment on its account -I believe the rewards greatly surpass the losses. I strongly believe that I would have not made it through this masters research, to the point of handing in this thesis, without the support of the great people around me that has carried me through it all. I therefore take this opportunity to sincerely thank each of these awesome people for their support. I have no words to express my gratitude to my supervisors, Dr. Corné van Daalen and Mr. Johann Treunicht, for giving me the opportunity to pursue this research under their able supervision. I know this might sound like a fairytale, but I always wanted to be Dr. van Daalen's student and do the cool stuff that he does from the first day I landed on the ESL webpage after completing my BEng degree at the University of Swaziland. Thank you Dr for your warm welcome from that very day and for your positive prospects for the possibility of that aspiration. Great thanks to Mr. Treunicht who offered me the bursary to work on this project two years later and who, without me asking, nominated Dr. van Daalen to co-supervise and be the primary supervisor of my project. Most importantly, I would like to thank both of them for their invaluable guidance, motivation and support throughout the duration of this research. I have indeed been standing on shoulders of giants. Great thanks also to Sandile Mkhaliphi (also known as Mr. Sharp), my fellow countryman, undergraduate classmate, masters lab-mate and probable future best man, for sharing the bursary advert with me. I would not have known of this opportunity, let alone working on this project, if you did not dare to share this information. Special thanks go to one of the coolest lecturers I have ever known, Dr. Japie Engelbrecht, for his input in expediting the processing of documents required for my visa application prior to the start of my first year. Thank you also for your constructive feedback during the course of my project and for constantly reassuring me that the end does come eventually -indeed it has come. I cannot help but admire your great sense of humour, which made me realise that being in academia does not make one a villain after all. Thanks also to Dr. Willem Jordaan, who used to call me "Bongi", and who constantly, and with genuine interest, kept on checking up on me throughout my time at the ESL. How can I forget to thank the rest of the robotic people at the ESL for their warm welcome and their support throughout this bumpy, but rewarding, research journey? Thank you all for making my stay pleasant, and for helping me gain a broader understanding of robotics through your different projects. I wish you all the best in your future endeavours. I would also like to specially thank the administration of the lab for keeping the periodic lab braiis and camps alive. Thank you for the free food, it was really appreciated! On that note, apologies for the few occasions where I remained behind, glued on my computer screen -acting like a nerd, when you guys went out. Still in the spirit of free stuff, I would like to thank the coffee machine administrator, Clint Lombard, for allowing me to default on payments when I did not have money, but still get my much-needed cups of coffee. God bless you sir! Thanks also to my officemates, Dinorego Mphogo and Joshua Mfiri, from whom I learnt a lot, not only about their perspectives on control systems and artificial intelligence, but also about deep life and survival principles. Particular thanks to Dino for always bringing home-made food for us to devour in the office. You really made our stay pleasant. The work presented in this thesis was performed in a number of places, most notably: three iv Stellenbosch University ACKNOWLEDGEMENTS v apartments I rented during my stay at Stellenbosch, my allocated office at the ESL, the Carnegie research commons at the J. S. Gericke library of Stellenbosch University, at home in Mpaka (Eswatini), on flight while travelling to Stellenbosch from home and vice versa, at the University of Johannesburg while on private visits, and at the University of the Witswatersrand while attending the Deep Learning Indaba conference. I would like to convey great thanks to everyone who made the environment conducive in these places for me to be able to conduct my work. To my three landlords at Stellenbosch, namely the Christians family, the Bennet family, and the Anolds family, I am grateful for making my stay in Stellenbosch feel like home. Thanks for every meal and moments of laughter you shared with me. I am grateful to Stellenbosch University for letting me use their world-class facilities, both in the ESL and at the Carnegie research commons. To my mom, who prepared homely meals and offered motherly support in all occasions I worked from home, I cannot thank you enough. Thanks also to every pilot who manned every aircraft I boarded for the smooth flights, which enabled me to do some of my work above the clouds! Great thanks to Abiola Bolaji who provided a very hospitable environment when I visited at the University of Johannesburg, allowing me to do a considerable portion of my work there. To the organisers of the Deep Learning Indaba conference, I am grateful for sponsoring my attendance of the conference, the opportunities to network with leading researchers in AI, the opportunity to present my work, the feedback I received and the prize that you awarded me. I appreciate everyone who did not hold back questions during the various presentations of the work contained in this thesis. Every question helped me rethink some aspects of the project and as such, each question reshaped this thesis in its own special way. Now, allow me to send my word of appreciation to the people who selflessly, and without expecting anything in return, helped me by reviewing the content of this thesis whenever I asked. Great thanks to both my supervisors for their informed, detailed and insightful reviews. I am also grateful to Feziwe Mamba, who did not mind sacrificing her time on numerous occasions for this purpose, when she would have otherwise spent it doing her own masters work in polymer science. Sandile Mkhaliphi has also been instrumental in this regard, and for that I am very grateful. I highly value the feedback I received from my mom, who was the first person to whom I demonstrated the work presented in this thesis in the form of simulations and videos for the different developed algorithms as well as the integrated...

This paper proposes a hybrid path planning algorithm incorporating a global and local search mechanism for mobile robot. The global path planning is based on Voronoi graph to establish a backbone path for the map with significantly reduced nodes for the original grid map. With the use of the backbone path, the D* algorithm is adopted to determine a shortest path between the starting and end points. Taking advantages of the D* algorithm and Voronoi graph, the proposed hybrid path planning algorithm is capable of obtaining a desired path for the mobile robot, overcoming the efficiency problem while maintaining maximum safety distance from the obstacles when the mobile robot navigates in the environment.

Robot motion planning problems are considered for boundary representation geometric models of curved planar and solid objects. We present algebraic algorithms to generate the boundary of configuration space obstacles arising from the translatory motion of objects among obstacles. To aid in the C-space generation various efficient computational geometry and algebraic geometry techniques need to be developed. We present algorithms to compute the convex hulls and various decompositions of planar curved objects. Finally, various motion planning problems are explored using these techniques.

This paper develops a novel computational method for the falsification of safety properties specified by syntactically safe linear temporal logic (LTL) formulas φ for hybrid systems with general nonlinear dynamics and input controls. The method is based on an effective combination of robot motion planning and model checking. Experiments on a hybrid robotic system benchmark with nonlinear dynamics show significant speedup over related work. The experiments also indicate significant speedup when using minimized DFA instead of non-minimized NFA, as obtained by standard tools, for representing the violating prefixes of φ.

We study the problem of designing control strategies for non-deterministic transitions systems enforcing the satisfaction of Linear Temporal Logic (LTL) formulas over their set of states. We focus on finite transition systems with inputs, which are often encountered when solving motion planning problems by using discrete quotients induced by a given partition of the state space. Our approach solves the problem conservatively using LTL games, and consists of the following three steps: (1) the original transition system is transformed into a transition system on which an LTL game can be played, (2) a solution of the LTL game on the new transition system is obtained, and (3) an interface between this solution and the initial transition system is constructed. The correctness of the method is ensured by design. The advantages and conservativeness of our approach are discussed and illustrated by simple examples.

In design standards and building codes such as the Uniform Building Code (UBC) (ICBO94) or the Americans with Disabilities Act Accessibility Guidelines (ADAAG) (ADAAG97), introductory provisions state the design intent or performance issues of a section, and subsequent prescriptive statements (provisions) outlining the methods to satisfy the design intent. Currently, prescriptive provisions are necessary to explicitly define a standard method to measure the design intent of a section of a design standard. As the provision statement becomes more prescriptive, the design intent is often lost or not fully captured. Consequently, ambiguity and inconsistency arise, thus making the design standard difficult to parse not only by computers, but for humans as well. This paper examines a design-intent approach to design standards processing to alleviate some of the difficulties and complexities of the code due to its prescriptive nature. By focusing on the design intent, it is possible to neg...

To facilitate natural and intuitive interactions with diverse user groups in real-world settings, social robots must be capable of addressing the varying requirements and expectations of these groups while adapting their behavior based on user feedback. While previous research often focuses on specific demographics, we present a novel framework for adaptive Human-Robot Interaction (HRI) that tailors interactions to different user groups and enables individual users to modulate interactions through both minor and major interruptions. Our primary contributions include the development of an adaptive, ROS-based HRI framework with an open-source code base. This framework supp orts natural interactions through advanced speech recognition and voice activity detection, and leverages a large language model (LLM) as a dialogue bridge. We validate the efficiency of our framework through module tests and system trials, demonstrating its high accuracy in age recognition and its robustness to repeated user inputs and plan changes.

We present a new sensor-based robot motion planning framework for mobile robot navigation in unknown environments. The main idea of the proposed planning approach, inspired by our recent works on using Harmonic Function-based Probabilistic Roadmaps (HFPRM) for robotic navigation in known environments (model-based cases) [1], [2], is to utilize a Fluid Dynamic (FD) paradigm based on potential flows to identify and prioritize critical regions, i.e. narrow passages and hard-to-navigate regions, at the scan planning stage of a sensor-based Probabilistic Roadmap (PRM). The PRM, which efficiently captures the connectivity of the free space, is incrementally expanded as the robot senses the physical workspace. Computer simulations and experimental results obtained using a mobile robot equipped with ultrasonic range finders are presented.

We present a new scheme for storing a planar graph in external memory so that any online path can be traversed in an I-O efficient way. Our storage scheme significantly improves the previous results for planar graphs with bounded face size. We also prove an upper bound on I-O efficiency of any storage scheme for well-shaped triangulated meshes. For these meshes, our storage scheme achieves optimal performance.

The textbook on Motion Planning “Principles of Robot Motion: Theory, Algorithms, and Implementations”, by H. Choset et al., MIT Press, appeared on June 2005, is reviewed and compared to other two textbooks on the same subject, from 1991 and 2006 respectively. The ground-breaking developments over the last decade justify the necessity of the newer textbooks, that appear to be complementary, despite some overlap in the contents. Peer Reviewed

We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation process, where the state process is affected by the modulation process only through an observation process, the observation process only observes the modulation process, and the modulation process is exogenous to control. We model this broad class of problems as a partially observed Markov decision process (POMDP). The belief function for the modulation process is control invariant, thus separating the estimation of the modulation process from the control of the state process. We call this specially structured POMDP the separable POMDP, or SEP-POMDP, and show it (i) can serve as a model for a broad class of application areas, e.g., inventory control, finance, healthcare systems, (ii) inherits value function and optimal policy structure from a set of co...

We revisit the classic problem of moving ladders of various lengths through a right-angled corridor. It has long been known that it is theoretically possible to tackle this problem through cylindrical algebraic decomposition (CAD): the valid positions of the ladder are described through polynomial equations and inequalities, which are then used to create a sign-invariant CAD. However, this formulation is too complex for use with current CAD technology, despite much progress in both CAD theory and hardware. We present a new formulation of the problem, by first considering the invalid positions of the ladder, negating this formula and using this as input for Qepcad (CAD software). We are then able to construct CADs for various lengths of ladder and analyse these through Qepcad's twodimensional plots functionality. We speculate on the reason our new formulation is more appropriate for the problem, suggest alternative formulations and discuss future work.

We discuss the following problem which arises in robot motion planning, NC machining and computer animation: Given are a fixed surface Ψ and N positions Φ i of a moving surface Φ such that the Φ i are in point contact with Ψ. Compute a smooth and fair Euclidean gliding motion Φ(t) of the surface Φ on the surface Ψ which interpolates (or approximates) the given positions Φ i at time instances t i. First we generalize interpolatory variational subdivision algorithms for curves to curves on surfaces. Second we study an unconstraint motion design algorithm which we then extend to the main contribution of this paper, an algorithm for the design of a motion constraint by a contacting surface pair. Both motion design algorithms use a feature point representation of the moving surface, subdivision algorithms for curves, instantaneous kinematics, and ideas from line geometry. Geometric methods are used for the numerical solution of the arising optimization problems.

Consensus formation tracking of multiple autonomous underwater vehicles (AUVs) subject to nonlinear and uncertain dynamics is a challenging problem in robotics. To tackle this challenge, a distributed bioinspired sliding mode controller is proposed in this paper. First, the conventional sliding mode controller (SMC) is presented, and the consensus problem is addressed on the basis of graph theory. Next, to tackle the high frequency chattering issue in SMC scheme and meanwhile improve the robustness to the noises, a bioinspired approach is introduced, in which a neural dynamic model is employed to replace the nonlinear sign or saturation function in the synthesis of conventional sliding mode controllers. Furthermore, the inputto-state stability of the resulting closed-loop system is proved in the presence of bounded lumped disturbance by the Lyapunov stability theory. Finally, simulation experiments are conducted to demonstrate the effectiveness of the proposed distributed formation control protocol.

The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.

Arrangement of lines is the subdivision of a plane by a finite set of lines. Arrangement is an important structure which can aid in solving many problems in theoretical computer science. Arrangement of lines also has important application in robot motion ...

The paper presents the conception of a soft control structure based on the time-optimal approach. Its parameters are selected in accordance with the rules of the statistical decision theory and additionally it allows the elimination of rapid changes in control values. The object is a basic mechanical system, with uncertain (also non-stationary) mass treated as a stochastic process. The methodology

We present a hybrid path planning algorithm for rigid bodies translating and rotating in a 3D workspace. Our approach generates a Voronoi roadmap in the workspace and combines it with "bridges" computed by a randomized path planner with Voronoi-biased sampling. The Voronoi roadmap is computed from a discrete approximation to the generalized Voronoi diagram (GVD) of the workspace, which is generated using graphics hardware. By this use of the GVD, portions of the path can be generated without random sampling, substantially reducing the number of random samples needed for the full query. The planner has been implemented and tested on a number of benchmarks. Some preliminary comparisons with a randomized motion planner indicate that our planner performs more than an order of magnitude faster in several challenging scenarios.

In this paper, we introduce an extension of our presented cognitive-based emotion model [27][28]and [30], where we enhance our knowledge-based emotion unit of the architecture by embedding a fuzzy rule-based system to it. The model utilizes the cognitive parameters dependency and their corresponding weights to regulate the robot's behavior and fuse their behavior data to achieve the final decision in their interaction with the environment. Using this fuzzy system, our previous model can simulate linguistic parameters for better controlling and generating understandable and flexible behaviors in the robots. We implement our model on an assistive healthcare robot, named Robot Nurse Assistant (RNA) and test it with human subjects. Our model records all the emotion states and essential information based on its predefined rules and learning system. Our results show that our robot interacts with patients in a reasonable, faithful way in special conditions which are defined by rules. T...

In this paper a multi-robot system (MRS) trajectory control for conducting a group of humans is proposed. Its architecture, implementation and the strategy to conduct people by a team of robots is discussed, as well as the robots motion planning methodology is being encompassed. Some experimental results on people localization by a vision system are also introduced, which exhibit its usage as sensory information for generation of people trajectory control. A social model to simulate humans motion is also included in this investigation as means to prove the mechanism of guidance and crowd dynamics by the team of robots, where such motion control is based on intelligent changes of position and speed.

This paper reports on a method and system which integrates human-computer interaction with reactive planning to operate a telerobot for use as an assistive device. The system is intended to meet the needs of individuals with physical disabilities and operate in an unstructured environment, rather than in a structured workcell. This allows the user considerable freedom and flexibility in terms of control and operating ease. We describe a novel approach for an intelligent assistive telerobotic system for such an environment: speech-deictic gesture control integrated with a knowledge-driven reactive planner and a stereo-vision system which builds a superquadric shape representation of the scene.

Geometric volumes can be used as an intermediate representation for bridging the gap between task planning, with its symbolic preconditions and effects, and motion planning, with its continuous-space geometry. In this work, we use sets of convex polyhedra to represent the boundaries of objects, robot manipulators, and swept volumes of robot motions. We apply efficient algorithms for convex decomposition, conservative swept volume approximation and collision detection, and integrate these methods into our existing "knowledge of volumes" approach to robot task planning called KVP. We demonstrate and evaluate our approach in several task planning scenarios, including a bimanual robot platform.

Start with Gott (2019)'s envelope polyhedron (Squares-4 around a point): a unit cube missing its top and bottom faces. Stretch by a factor of 2 in the vertical direction so its sides become (2 × 1 unit) rectangles. This has 8 faces (4 exterior, 4 interior), 8 vertices, and 16 edges. F −E +V = 0, implying a (toroidal) genus = 1. It is isometric to a flat square torus. Like any polyhedron it has zero intrinsic Gaussian curvature on its faces and edges. Since 4 right angled rectangles meet at each vertex, there is no angle deficit and zero Gaussian curvature there as well. All meridian and latitudinal circumferences are equal (4 units long).

We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions can be computed efficiently.

We propose HyDICE, Hybrid DIscrete Continuous Exploration, a multilayered approach for hybrid-system falsification that combines motion planning with discrete search and discovers safety violations by computing witness trajectories to unsafe states. The discrete search uses discrete transitions and a state-space decomposition to guide the motion planner during the search for witness trajectories. Experiments on a nonlinear hybrid robotic system with over one million modes and experiments with an aircraft conflict-resolution protocol with high-dimensional continuous state spaces demonstrate the effectiveness of HyDICE. Comparisons to related work show computational speedups of up to two orders of magnitude.

We present a biologically inspired approach for path planning with dynamic obstacle avoidance. Path planning is performed in a condensed configuration space of a robot generated by self-organizing neural networks (SONN). The robot itself and static as well as dynamic obstacles are mapped from the Cartesian task space into the configuration space by precomputed kinematics. The condensed space represents a cognitive map of the environment, which is inspired by place cells and the concept of cognitive maps in mammalian brains. The generation of training data as well as the evaluation were performed on a real industrial robot accompanied by simulations. To evaluate the reactive collision-free online planning within a changing environment, a demonstrator was realized. Then, a comparative study regarding sample-based planners was carried out. So we could show that the robot is able to operate in dynamically changing environments and re-plan its motion trajectories within impressing 0.02 seconds, which proofs the real-time capability of our concept.

We present a biologically inspired approach for path planning with dynamic obstacle avoidance. Path planning is performed in a condensed configuration space of a robot generated by self-organizing neural networks (SONN). The robot itself and static as well as dynamic obstacles are mapped from the Cartesian task space into the configuration space by precomputed kinematics. The condensed space represents a cognitive map of the environment, which is inspired by place cells and the concept of cognitive maps in mammalian brains. The generation of training data as well as the evaluation were performed on a real industrial robot accompanied by simulations. To evaluate the reactive collision-free online planning within a changing environment, a demonstrator was realized. Then, a comparative study regarding sample-based planners was carried out. So we could show that the robot is able to operate in dynamically changing environments and re-plan its motion trajectories within impressing 0.02 seconds, which proofs the real-time capability of our concept.

This work proposes a human motion prediction model for handover operations. We use in this work, the different phases of the handover operation to improve the human motion predictions. Our attention deep learning based model takes into account the position of the robot's End Effector and the phase in the handover operation to predict future human poses. Our model outputs a distribution of possible positions rather than one deterministic position, a key feature in order to allow robots to collaborate with humans. The attention deep learning based model has been trained and evaluated with a dataset created using human volunteers and an anthropomorphic robot, simulating handover operations where the robot is the giver and the human the receiver. For each operation, the human skeleton is obtained with an Intel RealSense D435i camera attached inside the robot's head. The results shown a great improvement of the human's right hand prediction and 3D body compared with other methods.

The core element of the symbol grounding problem is the instruction following task which is a dialogue based language game. The speaker gives a sequence of commands which have to be interpreted by the hearer. The dialog allows to solve complex problems from robotics which can't be addressed with backtracking algorithms from the past. From a programming perspective, the vocabulary of an instruction following game has much in common with the opcodes in Assembly language used to program computers on the lowest level. The idea is that a high level input language gets converted into a low level machine language. This transformation is done by an interpreter which is a grounding mechanism. In addition to the previous two articles about the symbol grounding problem, this part III gives an overview about the origin and how it may help to build future robots.

In this paper, we consider the problem of robot motion planning in order to satisfy formulas expressible in temporal logics. Temporal logics naturally express traditional robot specifications such as reaching a goal or avoiding an obstacle, but also more sophisticated specifications such as sequencing, coverage, or temporal ordering of different tasks. In order to provide computational solutions to this problem, we first construct discrete abstractions of robot motion based on some environmental decomposition. We then generate discrete plans satisfying the temporal logic formula using powerful model checking tools, and finally translate the discrete plans to continuous trajectories using hybrid control. Critical to our approach is providing formal guarantees ensuring that if the discrete plan satisfies the temporal logic formula, then the continuous motion also satisfies the exact same formula.

In this paper we analyze some relationships between the topological complexity of a space X and the category of C∆ X , the homotopy cofibre of the diagonal map ∆X : X → X × X. We establish the equality of the two invariants for several classes of spaces including the spheres, the H-spaces, the real and complex projective spaces and almost all the (standard) lens spaces.

Mobile robots are the robots that can move through the environment and be used in many applications, including the industrial environment, planet exploration, warehousing, and daily household chores. They can be controlled by an operator, set to do some specific jobs, or work autonomously. Robot path planning is the task of an autonomous robot to move safely from one position to another. In this paper, three new objective functions are introduced in the structure of improved grey wolf optimizer (IGWO) and improved particle swarm optimization (IPSO) for the robot path planning problems. As another part of our proposed method, a reduction of laser range finder (LRF) data is performed, and the avoidance collision approach is also introduced. Robots determine the next position by using LRF data and IGWO (IPSO) algorithms in a local approach. The initial and the goal positions are predefined for each robot. Moreover, the location of static obstacles and other robots are unknown for each robot. Finally, the experimental results of the robot path planning using IGWO are compared to different algorithms. The results indicate that the proposed method performs better in determining an optimal, short, safe, and smooth path. Also, it has less power and time consumption than other methods. All the algorithms are implemented in the V-REP robot simulator.

Given a set of radii measured from a fixed point, the existence of a convex configuration with respect to the set of distinct radii in the twodimensional case is proved when radii are distinct or repeated at most four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.

In this paper, we construct an algorithm for determining whether a given tessellation on a sphere is a spherical Laguerre Voronoi diagram or not. For spherical Laguerre tessellations, not only the locations of the Voronoi generators, but also their weights are required to recover. However, unlike the ordinary spherical Voronoi diagram, the generator set is not unique, which makes the problem difficult. To solve the problem, we use the property that a tessellation is a spherical Laguerre Voronoi diagram if and only if there is a polyhedron whose central projection coincides with the tessellation. We determine the degrees of freedom for the polyhedron, and then construct an algorithm for recognizing Laguerre tessellations.

In this paper we consider the Voronoï Diagram of a finite family of parallel half-lines, with the same orientation, constrained to a compact domain D 0 ⊂ R 3 , with respect to the Euclidean distance. We present an efficient approximation algorithm for computing such VD, using a subdivision process, which produces a mesh representing the topology of the VD in D 0. The computed topology may not be correct for degenerate configurations or configurations close to degenerate. In this case, the output is a valid partition, which is close to the exact partition in Voronoï cells if the input data were given with no error. We also present the result of an implementation in Julia language with visualization using Axl software (axl.inria.fr) of the algorithm. Some examples and analysis are shown.

Motion planning in continuous space is a fundamental robotics problem that has been approached from many perspectives. Rapidly-exploring Random Trees (RRTs) use sampling to efficiently traverse the continuous and high-dimensional state space. Heuristic graph search methods use lower bounds on solution cost to focus effort on portions of the space that are likely to be traversed by low-cost solutions. In this paper, we bring these two ideas together in a technique called f-biasing: we use estimates of solution cost, computed as in heuristic search, to guide sparse sampling, as in RRTs. Estimates of solution cost are quickly computed using an abstract version of the problem, then an RRT is constructed by biasing the sampling toward areas of the space traversed by low cost solutions under the abstraction. We show that f-biasing maintains all of the desirable theoretical properties of RRT and RRT*, such as completeness and asymptotic convergence to optimality. We also present experimental results showing that f-biasing finds cheaper paths faster than previous techniques. We see this new technique as strengthening the connections between motion planning in robotics and combinatorial search in artificial intelligence.

In telemanipulation, showing the user multiple views of the remote environment can offer many benefits, although such different views can also create a problem for control. Systems must either choose a single fixed control frame, aligned with at most one of the views or switch between view-aligned control frames, enabling view-aligned control at the expense of switching costs. In this paper, we explore the trade-off between these options. We study the feasibility, benefits, and drawbacks of switching the user's control frame to align with the actively used view during telemanipulation. We additionally explore the effectiveness of explicit and implicit methods for switching control frames. Our results show that switching between multiple viewspecific control frames offers significant performance gains compared to a fixed control frame. We also find personal preferences for explicit or implicit switching based on how participants planned their movements. Our findings offer concrete design guidelines for future multi-camera interfaces.

Manipulations of a constrained object often use a non-rigid grasp that allows the object to rotate relative to the end effector. This orientation slip strategy is often present in natural human demonstrations, yet it is generally overlooked in methods to identify constraints from such demonstrations. In this paper, we present a method to model and recognize prehensile orientation slip in human demonstrations of constrained interactions. Using only observations of an end effector, we can detect the type of constraint, parameters of the constraint, and orientation slip properties. Our method uses a novel hierarchical model selection method that is informed by multiple origins of physics-based evidence. A study with eight participants shows that orientation slip occurs in natural demonstrations and confirms that it can be detected by our method.

This paper proposes a stable sparse rapidlyexploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest cost among all the vertices within the neighborhood of a randomly selected sample and then extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. In addition, HySST maintains a static set of witness points such that all the vertices within the neighborhood of each witness are pruned except the vertex with the lowest cost. Through a definition of concatenation of functions defined on hybrid time domains, we show that HySST is asymptotically near optimal, namely, the probability of failing to find a motion plan such that its cost is close to the optimal cost approaches zero as the number of iterations of the algorithm increases to infinity. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The proposed algorithm is applied to an actuated bouncing ball system and a collisionresilient tensegrity multicopter system so as to highlight its generality and computational features.

Mobile telepresence robots (MTRs) have become increasingly popular in the expanding world of remote work, providing new avenues for people to actively participate in activities at a distance. However, humans operating MTRs often have difficulty navigating in densely populated environments due to limited situation awareness and narrow field-of-view, which reduces user acceptance and satisfaction. Shared autonomy in navigation has been studied primarily in static environments or in situations where only one pedestrian interacts with the robot. We present a multimodal shared autonomy approach, leveraging visual and haptic guidance, to provide navigation assistance for remote operators in densely-populated environments. It uses a modified form of reciprocal velocity obstacles for generating safe control inputs while taking social proxemics constraints into account. Two different visual guidance designs, as well as haptic force rendering, were proposed to convey safe control input. We conducted a user study to compare the merits and limitations of multimodal navigation assistance to haptic or visual assistance alone on a shared navigation task. The study involved 15 participants operating a virtual telepresence robot in a virtual hall with moving pedestrians, using the different assistance modalities. We evaluated navigation performance, transparency and cooperation, as well as user preferences. Our results showed that participants preferred multimodal assistance with a visual guidance trajectory over haptic or visual modalities alone, although it had no impact on navigation performance. Additionally, we found that visual guidance trajectories conveyed a higher degree of understanding and cooperation than equivalent haptic cues in a navigation task.

In a recent publication [14] we have introduced a new method, based on the Lusternik-Schnirelmann category and the cohomology ring of a space X, that yields lower bounds for the size of a triangulation of X. In this paper we present an important extension that takes into account the fundamental group of X. In fact, if π1(X) contains elements of finite order, then one can often find cohomology classes of high 'category weight', which in turn allow for much stronger estimates of the size of triangulations of X. We develop several weighted estimates and then apply our method to compute explicit lower bounds for the size of triangulations of orbit spaces of cyclic group actions on a variety of spaces including products of spheres, Stiefel manifolds, Lie groups and highly-connected manifolds.

The topological complexity is a numerical invariant which measures the number of commands an autonomous robot needs in order to move in a space to perform a task. To explain these ideas, we will walk through the various algebraic definitions and provide physical examples along the way. We calculate the topological complexity for various scenarios, starting with a single robot moving on a simple space, we will add on to this scenario towards a final case including more robots and more complicated spaces where they move. Finally, we provide an example where two driverless vehicles move in a track joining seven colleges throughout Chicago. We determine the number of instructions as well as their content for this case study.

This paper presents a sampling-based method for path planning in robotic systems without known cost-to-go information. It uses trajectories generated from random search to heuristically learn the cost-to-go of regions within the configuration space. Gradually, the search is increasingly directed towards lower cost regions of the configuration space, thereby producing paths that converge towards the optimal path. The proposed framework builds on Rapidly-exploring Random Trees for random sampling-based search and Reinforcement Learning is used as the learning method. A series of experiments were performed to evaluate and demonstrate the performance of the proposed method.

This paper intoduces a preliminary study on a new control decomposition criterion for collaborative teleoperation systems - field of view deficiency. This criterion represents the amount of visual information available to operators. As a tool for such decomposition we introduce a dominance distribution matrix - a more flexible approach to dominance distribution than a well-known scalar dominance factor concept. We introduce collaborative teleoperation architecture, based on field of view deficiency criterion and apply it to experimental dual-master/single-slave teleoperation system. Experimental study demonstrates the effectiveness of the proposed approaches.