SwePub - sökning: WFRF:(Ögren Petter)

Numrering	Referens	Omslagsbild	Hitta
1.	Anisi, David A., et al. (författare) Cooperative Minimum Time Surveillance With Multiple Ground Vehicles 2010 Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 55:12, s. 2679-2691 Tidskriftsartikel (refereegranskat)abstract In this paper, we formulate and solve two different minimum time problems related to unmanned ground vehicle (UGV) surveillance. The first problem is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensors' field of view are assumed to have a limited coverage range and be occluded by the obstacles. The second problem extends the first by additionally requiring the induced information graph to be connected at the time instants when the UGVs perform the surveillance mission, i.e., when they gather and transmit sensor data. In the context of the second problem, we also introduce and utilize the notion of recurrent connectivity, which is a significantly more flexible connectivity constraint than, e.g., the 1-hop connectivity constraints and use it to discuss consensus filter convergence for the group of UGVs.
2.	Bull, Peter, et al. (författare) Förstudie obemannade farkoster 2012 Rapport (populärvet., debatt m.m.)abstract Obemannade farkoster används allt oftare, och i allt fler roller, i dagens kon- flikter. Denna rapport ger en bred överblick över området militära obemannade farkoster, samt rekommendationer för inriktningen av framtida FoU-satsningar inom området.Överblicken över området har fokus på både system, förmågor och verksam- heter som är relevanta för Försvarsmakten. Genom att låta de insatsförmågor som definieras i FMUP (Försvarsmaktens utvecklingsplan) gå som en röd tråd genom rapporten, både när specifika system diskuteras och när möjliga scena- rier där obemannade farkoster kan vara till nytta beskrivs, har vi försökt hålla både bredd och relevans i dokumentet.Rekommendationerna vilar på en genomgång av de inriktningsdokument som producerats i Försvarsmakten, t.ex. Perspektivplanneringen och FMUP, besök vid de enheter som dagligen använder obemannade farkoster, UAV-enheten i Karlsborg och Swedec i Eksjö, samt den områdesöverblick som nämns ovan. Slutsatserna är att den effektivaste kompetensuppbyggnaden och kunskapsöver- föringen fås om man skapar breda tvärvetenskapliga projekt inom respektive systemkategori (UAV, UGV, etc) med nära kontakter till materielförsörjnings- processen och perspektivplaneringen. Dessa kan samla kompetensen inom FHS och FOI, övervaka forskningsfronten genom att bevaka tävlingar, konferenser samt delta i internationella samarbeten, samt överföra det samlade resultaten till Försvarsmakten genom demonstrationer av verkliga eller simulerade delsy- stem och interaktiva simuleringar av hela system. Just systemsimuleringar kan göras särskilt realistiska, eftersom interaktionen med de riktiga obemannade systemen till stor del sker igenom kontrollstationernas datorer. På så sätt ska- pas en känsla för både hot och möjligheter med de nya systemen, vilket gagnar både taktikutveckling och materielprocesser.
3.	Colledanchise, Michele, et al. (författare) How Behavior Trees Modularize Robustness and Safety in Hybrid Systems 2014 Ingår i: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, (IROS 2014). - : IEEE. - 9781479969340 ; , s. 1482-1488 Konferensbidrag (refereegranskat)abstract Behavior Trees (BTs) have become a popular framework for designing controllers of in-game opponents in the computer gaming industry. In this paper, we formalize and analyze the reasons behind the success of the BTs using standard tools of robot control theory, focusing on how properties such as robustness and safety are addressed in a modular way. In particular, we show how these key properties can be traced back to the ideas of subsumption and sequential compositions of robot behaviors. Thus BTs can be seen as a recent addition to a long research effort towards increasing modularity, robustness and safety of robot control software. To illustrate the use of BTs, we provide a set of solutions to example problems.
4.	Colledanchise, Michele, et al. (författare) Obstacle avoidance in formation using navigation-like functions and constraint based programming 2013 Ingår i: Proceedings of the International Conference on Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ. - : IEEE conference proceedings. - 9781467363587 ; , s. 5234-5239 Konferensbidrag (refereegranskat)abstract In this paper, we combine navigation functionlike potential fields and constraint based programming to achieve obstacle avoidance in formation. Constraint based programming was developed in robotic manipulation as a technique to take several constraints into account when controlling redundant manipulators. The approach has also been generalized, and applied to other control systems such as dual arm manipulators and unmanned aerial vehicles. Navigation functions are an elegant way to design controllers with provable properties for navigation problems. By combining these tools, we take advantage of the redundancy inherent in a multi-agent control problem and are able to concurrently address features such as formation maintenance and goal convergence, even in the presence of moving obstacles. We show how the user can decide a priority ordering of the objectives, as well as a clear way of seeing what objectives are currently addressed and what are postponed. We also analyze the theoretical properties of the proposed controller. Finally, we use a set of simulations to illustrate the approach.
5.	Colledanchise, Michele, 1987-, et al. (författare) Robot navigation under uncertainties using event based sampling 2014 Ingår i: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on. - : IEEE conference proceedings. ; , s. 1438-1445 Konferensbidrag (refereegranskat)abstract In many robot applications, sensor feedback is needed to reduce uncertainties in environment models. However, sensor data acquisition also induces costs in terms of the time elapsed to make the observations and the computations needed to find new estimates. In this paper, we show how to use event based sampling to reduce the number of measurements done, thereby saving time, computational resources and power, without jeopardizing critical system properties such as safety and goal convergence. This is done by combining recent advances in nonlinear estimation with event based control using artificial potential fields. The results are particularly useful for real time systems such as high speed vehicles or teleoperated robots, where the cost of taking measurements is even higher, in terms of stops or transmission times. We conclude the paper with a set of simulations to illustrate the effectiveness of the approach and compare it with a baseline approach using periodic measurements.
6.	Erlandsson, Tina, 1983- (författare) A combat survivability model for evaluating air mission routes in future decision support systems 2014 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)
7.	Karayiannidis, Yiannis, 1980-, et al. (författare) Adaptive force/velocity control for opening unknown doors 2012 Ingår i: Robot Control, Volume 10, Part 1. - 9783902823113 ; , s. 753-758 Konferensbidrag (refereegranskat)abstract The problem of door opening is fundamental for robots operating in domesticenvironments. Since these environments are generally unstructured, a robot must deal withseveral types of uncertainties associated with the dynamics and kinematics of a door to achievesuccessful opening. The present paper proposes a dynamic force/velocity controller which usesadaptive estimation of the radial direction based on adaptive estimates of the door hinge’sposition. The control action is decomposed into estimated radial and tangential directions,which are proved to converge to the corresponding actual values. The force controller usesreactive compensation of the tangential forces and regulates the radial force to a desired smallvalue, while the velocity controller ensures that the robot’s end-effector moves with a desiredtangential velocity. The performance of the control scheme is demonstrated in simulation witha 2 DoF planar manipulator opening a door.
8.	Karayiannidis, Yiannis, 1980-, et al. (författare) Design of force-driven online motion plans for door opening under uncertainties 2012 Ingår i: Workshop on Real-time Motion Planning: Online, Reactive, and in Real-time. Konferensbidrag (refereegranskat)abstract The problem of door opening is fundamental for household robotic applications. Domestic environments are generally less structured than industrial environments and thus several types of uncertainties associated with the dynamics and kinematics of a door must be dealt with to achieve successful opening. This paper proposes a method that can open doors without prior knowledge of the door kinematics. The proposed method can be implemented on a velocity-controlled manipulator with force sensing capabilities at the end-effector. The velocity reference is designed by using feedback of force measurements while constraint and motion directions are updated online based on adaptive estimates of the position of the door hinge. The online estimator is appropriately designed in order to identify the unknown directions. The proposed scheme has theoretically guaranteed performance which is further demonstrated in experiments on a real robot. Experimental results additionally show the robustness of the proposed method under disturbances introduced by the motion of the mobile platform.
9.	Karayiannidis, Yiannis, 1980-, et al. (författare) Interactive perception and manipulation of unknown constrained mechanisms using adaptive control 2013 Ingår i: ICRA 2013 Mobile Manipulation Workshop on Interactive Perception. Konferensbidrag (refereegranskat)
10.	Karayiannidis, Yiannis, 1980-, et al. (författare) Model-free robot manipulation of doors and drawers by means of fixed-grasps 2013 Ingår i: 2013 IEEE International Conference on Robotics and Automation (ICRA). - New York : IEEE. - 9781467356411 ; , s. 4485-4492 Konferensbidrag (refereegranskat)abstract This paper addresses the problem of robot interaction with objects attached to the environment through joints such as doors or drawers. We propose a methodology that requires no prior knowledge of the objects’ kinematics, including the type of joint - either prismatic or revolute. The method consists of a velocity controller which relies onforce/torque measurements and estimation of the motion direction,rotational axis and the distance from the center of rotation.The method is suitable for any velocity controlled manipulatorwith a force/torque sensor at the end-effector. The force/torquecontrol regulates the applied forces and torques within givenconstraints, while the velocity controller ensures that the endeffectormoves with a task-related desired tangential velocity. The paper also provides a proof that the estimates converge tothe actual values. The method is evaluated in different scenarios typically met in a household environment.
11.	Karayiannidis, Yiannis, 1980-, et al. (författare) "Open Sesame!" Adaptive Force/Velocity Control for Opening Unknown Doors 2012 Ingår i: Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on. - : IEEE. - 9781467317375 ; , s. 4040-4047 Konferensbidrag (refereegranskat)abstract The problem of door opening is fundamental for robots operating in domestic environments. Since these environments are generally less structured than industrial environments, several types of uncertainties associated with the dynamics and kinematics of a door must be dealt with to achieve successful opening. This paper proposes a method that can open doors without prior knowledge of the door kinematics. The proposed method can be implemented on a velocity-controlled manipulator with force sensing capabilities at the end-effector. The method consists of a velocity controller which uses force measurements and estimates of the radial direction based on adaptive estimates of the position of the door hinge. The control action is decomposed into an estimated radial and tangential direction following the concept of hybrid force/motion control. A force controller acting within the velocity controller regulates the radial force to a desired small value while the velocity controller ensures that the end effector of the robot moves with a desired tangential velocity leading to task completion. This paper also provides a proof that the adaptive estimates of the radial direction converge to the actual radial vector. The performance of the control scheme is demonstrated in both simulation and on a real robot.
12.	Katsilieris, Fotios, et al. (författare) Demonstration of multi-robot search and secure 2010 Konferensbidrag (refereegranskat)abstract We consider the search and secure problem, where intruders are to be detected in a bounded area without allowing them to escape. The problem is tackled by representing the area to be searched as a traversability graph, which is reduced to a tree graph by placing stationary robots to remove loops. The search of the remaining tree is performed using two strategies that represent different trade-offs between the needed search time and the number of robots. Proof of correctness is provided for these two strategies. The proposed algorithm was implemented and demonstrated as part of an outfield experiment involving a team of Rotundus spherical robots.
13.	Marzinotto, Alejandro, et al. (författare) Towards a Unified Behavior Trees Framework for Robot Control 2014 Ingår i: Robotics and Automation (ICRA), 2014 IEEE International Conference on<em> </em>. - : IEEE Robotics and Automation Society. ; , s. 5420-5427 Konferensbidrag (refereegranskat)abstract This paper presents a unified framework for Behavior Trees (BTs), a plan representation and execution tool. The available literature lacks the consistency and mathematical rigor required for robotic and control applications. Therefore, we approach this problem in two steps: first, reviewing the most popular BT literature exposing the aforementioned issues; second, describing our unified BT framework along with equivalence notions between BTs and Controlled Hybrid Dynamical Systems (CHDSs). This paper improves on the existing state of the art as it describes BTs in a more accurate and compact way, while providing insight about their actual representation capabilities. Lastly, we demonstrate the applicability of our framework to real systems scheduling open-loop actions in a grasping mission that involves a NAO robot and our BT library.
14.	Robinson, John, et al. (författare) On the use of gradual dense-sparse discretizations in receding horizon control 2014 Ingår i: Optimal control applications & methods. - : Wiley-Blackwell. - 0143-2087 .- 1099-1514. ; 35:3, s. 253-270 Tidskriftsartikel (refereegranskat)abstract A key factor to success in implementations of real time optimal control, such as receding horizon control (RHC), is making efficient use of computational resources. The main trade-off is then between efficiency and accuracy of each RHC iteration, and the resulting overall optimality properties of the concatenated iterations, that is, how closely this represents a solution to the underlying infinite time optimal control problem (OCP). Both these issues can be addressed by adapting the RHC solution strategy to the expected form of the solution. Using gradual dense-sparse (GDS) node distributions in direct transcription formulations of the finite time OCP solved in each RHC iteration is a way of adapting the node distribution of this OCP to the fact that it is actually part of an RHC scheme. We have previously argued that this is reasonable, because the near future plan must be implemented now, but the far future plan can and will be revised later. In this paper, we investigate RHC applications where the asymptotic qualitative behavior of the OCP solution can be analyzed in advance. For some classes of systems, explicit exponential convergence rates of the solutions can be computed. We establish such convergence rates for a class of control affine nonlinear systems with a locally quadratic cost and propose to use versions of GDS node distributions for such systems because they will (eventually) be better adapted to the form of the solution. The advantages of the GDS approach in such settings is illustrated with simulations.
15.	Salling, E., et al. (författare) Learning air combat parameters using differential evolution 2013 Ingår i: Frontiers in Artificial Intelligence and Applications. - : IOS Press. - 9781614993292 ; , s. 225-234 Konferensbidrag (refereegranskat)abstract In this paper, we improve the performance of autonomous air combat behaviours using a differential evolution approach. We have previously developed air combat behaviours, that are used as opponents in a pilot training facility of the Swedish Air Force. These behaviours contain a number of design parameters, such as at what distance to fire missiles and what risk levels toaccept before disengaging. We improve the performance of the behaviours by applying two approaches. First, by searching for the best response against a given opponent strategy, second by looking for a Nash-equilibrium in a game where both players are allowed to adapt their strategies. Differential Evolution is used in both cases, and the fitness of the parameters is evaluated using parallel execution of detailed high fidelity models of aircraft, weapons and behaviours.
16.	Thunberg, Johan, et al. (författare) A Boolean Control Network Approach to Pursuit Evasion Problems in Polygonal Environments 2011 Ingår i: 2011 IEEE International Conference on obotics and Automation (ICRA). - 9781612843865 ; , s. 4506-4511 Konferensbidrag (refereegranskat)abstract In this paper, the multi pursuer version of the pursuit evasion problem in polygonal environments is addressed. This problem is NP-hard, and therefore we seek good enough, but not optimal solutions. By modeling the problem as a Boolean Control Network, we can efficiently keep track of which regions are cleared, and which are not, while the input nodes of the network are used to represent the motion of the pursuers. The environment is partitioned into a set of convex regions, where each region correspond to a set of nodes in the network. The method is implemented in ANSI C, and efficiently solves complex environments containing multiple loops and requiring so-called recontamination. The provided examples demonstrate the effectiveness of the method in terms of computational time
17.	Thunberg, Johan, et al. (författare) A Mixed Integer Linear Programming approach to Pursuit Evasion Problems with optional Connectivity Constraints 2011 Ingår i: Autonomous Robots. - : Springer Science and Business Media LLC. - 0929-5593 .- 1573-7527. ; 31:4, s. 333-343 Tidskriftsartikel (refereegranskat)abstract In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so-called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi pursuer pursuit evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples.
18.	Thunberg, Johan, et al. (författare) An Iterative Mixed Integer Linear Programming Approach to Pursuit Evasion Problems in Polygonal Environments 2010 Ingår i: 2010 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA). - 9781424450404 ; , s. 5498-5503 Konferensbidrag (refereegranskat)abstract In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. It is well known that this problem is NP-hard, and therefore we seek efficient, but not optimal, solutions by relaxing the problem and applying the tools of Mixed Integer Linear Programming (MILP) and Receding Horizon Control (RHC). Approaches using MILP and RHC are known to produce efficient algorithms in other path planning domains, such as obstacle avoidance. Here we show how the MILP formalism can be used in a pursuit evasion setting to capture the motion of the pursuers as well as the partitioning of the pursuit search region into a cleared and a contaminated part. RHC is furthermore a well known way of balancing performance and computation requirements by iteratively solving path planning problems over a receding planning horizon, and adapt the length of that horizon to the computational resources available. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples.
19.	Wang, Yuquan, 1985-, et al. (författare) A Distributed Convergent Solution to the Ambulance Positioning Problem on a Streetmap Graph 2014 Konferensbidrag (refereegranskat)abstract In this paper, we combine ideas from multi-agent cooperative coverage control, with problem formulations from the resource allocation field, to create a distributed convergent approach to the ambulance positioning problem. Inspired by coverage control we use the graph version of so-called Voronoi regions, making the solution distributed and reactive, thereby freeing computational resources. The solution is distributed in the sense that each vehicle only needs to know the positions of its neighbors, and the computations of each vehicle only depend on the size of its Voronoi region/set. This implies that considering a problem of twice the size, using twice the number of vehicles will leave the computational load per vehicle unchanged. The freed resources are used to capture the allocation problem in more detail: maximizing an estimate of the victim survival probability instead of more coarse measures of ambulance availability. Using real city street map data from OpenStreetMap (OSM), we provide simulation results illustrating the applicability of our approach. Finally, we prove that the proposed distributed algorithm is convergent in the sense that it finds a local optimum in finite time.
20.	Wang, Yuquan, 1985-, et al. (författare) Singularity analysis of closed-loop inverse kinematics algorithms with respect to manipulator geometric uncertainties 2014 Annan publikation (övrigt vetenskapligt/konstnärligt)
21.	Wang, Yuquan, 1985-, et al. (författare) Whole body control of a dual-arm mobile robot using a virtual kinematic chain 2014 Annan publikation (övrigt vetenskapligt/konstnärligt)
22.	Ögren, Petter, et al. (författare) A Model Based Approach to Modular Multi-Objective Robot Control 2011 Ingår i: Journal of Intelligent and Robotic Systems. - : Springer Netherlands. - 0921-0296 .- 1573-0409. ; 63:2, s. 257-282 Tidskriftsartikel (refereegranskat)abstract Two broad classes of robot controllers are the modular, and the model based approaches. The modular approaches include the Reactive or Behavior Based designs. They do not rely on mathematical system models, but are easy to design, modify and extend. In the model based approaches, a model is used to design a single controller with verifiable system properties. The resulting designs are however often hard to extend, without jeopardizing the previously proven properties. This paper describes an attempt to narrow the gap between the flexibility of the modular approaches, and the predictability of the model based approaches, by proposing a modular design that does the combination, or arbitration, of the different modules in a model based way. By taking the (model based) time derivatives of scalar, Lyapunov-like, objective functions into account, the arbitration module can keep track of the time evolution of the objectives. This enables it to handle objective tradeoffs in a predictable way by finding controls that preserve an important objective that is currently met, while striving to satisfy another, less important one that is not yet achieved. To illustrate the approach a UAV control problem from the literature is solved, resulting in comparable, or better, performance.
23.	Ögren, Petter, 1974-, et al. (författare) A Multi Objective Control Approach to Online Dual Arm Manipulation 2012 Ingår i: Robot Control. - : International Federation of Automatic Control. - 9783902823113 ; , s. 747-752 Konferensbidrag (refereegranskat)abstract In this paper, we propose a new way to exploit the redundancy of dual arm mobile manipulators when performing inherently bi-manual tasks using online controllers. Bi-manual tasks are tasks that require motion of both arms in order to be carried out efficiently, such as holding and cleaning an object, or moving an object from one hand to the other. These tasks are often associated with several constraints, such as singularity- and collision avoidance, but also a high degree of redundancy, as the relative positions of the two grippers is far more important than the absolute positions, when for example handing an object from one arm to the other. By applying a modular multi objective control framework, inspired by earlier work on sub-task control, we exploit this redundancy to form a subset of the joint space that is feasible, i.e. not violating any of the constraints. Earlier approacher added the additional tasks in terms of equality constraints, thereby reducing the dimension of the feasible subset until it was a single point. Here however, we add the additional tasks in terms of inequalities, removing parts of the feasible set rather than collapsing its dimensionality. Thus, we are able to handle an arbitrary number of constraints, instead of a number corresponding to the dimension of the feasible set (degree of redundancy). Finally, inside the feasible set we choose controls stay in the set, while simultaneously minimizing some given objective. The proposed approach is illustrated by several simulation examples.
24.	Ögren, Petter, 1974-, et al. (författare) Design and implementation of a new teleoperation control mode for differential drive UGVs 2014 Ingår i: Autonomous Robots. - : Springer Science and Business Media LLC. - 0929-5593 .- 1573-7527. ; 37:1, s. 71-79 Tidskriftsartikel (refereegranskat)abstract In this paper, we propose and implement a new control mode for teleoperated unmanned ground vehicles (UGVs), that exploits the similarities between computer games and teleoperation robotics. Today, all teleoperated differential drive UGVs use a control mode called Tank Control, in which the UGV chassis and the pan tilt camera are controlled separately. This control mode was also the dominating choice when the computer game genre First Person Shooter (FPS) first appeared. However, the hugely successful FPS genre, including titles such as Doom, Half Life and Call of Duty, now uses a much more intuitive control mode, Free Look Control (FLC), in which rotation and translation of the character are decoupled, and controlled separately. The main contribution of this paper is that we replace Tank Control with FLC in a real UGV. Using feedback linearization, the orientation of the UGV chassis is abstracted away, and the orientation and translation of the camera are decoupled, enabling the operator to use FLC when controlling the UGV. This decoupling is then experimentally verified. The developments in the gaming community indicates that FLC is more intuitive than Tank Control and reduces the well known situational awareness problem. It furthermore reduces the need for operator training, since literary millions of future operators have already spent hundreds of hours using the interface.
25.	Ögren, Petter, 1974- (författare) Increasing Modularity of UAV Control Systems using Computer Game Behavior Trees 2012 Ingår i: AIAA Guidance, Navigation, and Control Conference 2012. - 9781600869389 Konferensbidrag (refereegranskat)abstract In this paper, we argue that the modularity, reusability and complexity of Unmanned Aerial Vehicle (UAV) guidance and control systems might be improved by using a Behavior Tree (BT) architecture. BTs are a particular kind of Hybrid Dynamical Systems (HDS), where the state transitions of the HDS are implicitly encoded in a tree structure, instead of explicitly stated in transition maps. In the gaming industry, BTs have gained a lot of interest, and are now replacing HDS in the control architecture of many automated in-game opponents. Below, we explore the relationship between HDS and BTs. We show that any HDS can be written as a BT and that many common UAV control constructs are quite naturally formulated as BTs. Finally, we discuss the positive implications of making the above mentioned state transitions implicit in the BTs.
26.	Ögren, Petter, et al. (författare) Receding Horizon Control of UAVs using Gradual Dense-Sparse Discretizations 2010 Konferensbidrag (refereegranskat)abstract In this paper we propose a way of increasing the eciency of some direct Receding Horizon Control (RHC) schemes. The basic idea is to adapt the allocation of compu- tational resources to how the iterative plans are used. By using Gradual Dense-Sparse discretizations (GDS), we make sure that the plans are detailed where they need to be, i.e., in the very near future, and less detailed further ahead. The gradual transition in discretization density re ects increased uncertainty and reduced need for detail near the end of the planning horizon. The proposed extension is natural, since the standard RHC approach already contains a computational asymmetry in terms of the coarse cost-to-go computations and the more detailed short horizon plans. Using GDS discretizations, we bring this asymmetry one step further, and let the short horizon plans themselves be detailed in the near term and more coarse in the long term. The rationale for dierent levels of detail is as follows. 1) Near future plans need to be implemented soon, while far future plans can be rened or revised later. 2) More accurate sensor information is available about the system and its surroundings in the near future, and detailed planning is only rational in low uncertainty situations. 3) It has been shown that reducing the node density in the later parts of xed horizon optimal control problems gives a very small reduction in the solution quality of the rst part of the trajectory. The reduced level of detail in the later parts of a plan can increase the eciency of the RHC in two ways. If the discretization is made sparse by removing nodes, fewer computations are necessary, and if the discretization is made sparse by spreading the last nodes over a longer time-horizon, the performance will be improved.

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