Rendezvous Time Research Articles

Efficacy and safety of the needle rendezvous technique for infrainguinal arterial calcified lesions

BackgroundLower extremity artery disease is increasingly prevalent, and complex lesions such as calcified chronic total occlusions pose significant challenges during endovascular therapy. The needle rendezvous technique, which involves puncturing a needle toward the guidewire within the lesion or lumen and advancing the guidewire into the needle lumen to achieve guidewire externalization, offers a potential solution. If device passage remains challenging, the Rendezvous-PIERCE technique can be subsequently employed by advancing the needle over the externalized guidewire to modify the lesion directly. This study aimed to evaluate the procedural outcomes of needle rendezvous in infrainguinal arterial occlusive lesions.MethodsThis single-center, retrospective, single-arm study included patients treated with needle rendezvous between August 2020 and March 2024. The primary outcome was technical success rate, defined as the device passage following guidewire externalization using needle rendezvous. Secondary outcomes included the rates of procedural success, complications, and 30-day clinical-driven target lesion revascularization (CDTLR).ResultsTwenty-five patients (25 limbs) with 52% on hemodialysis and 80% having chronic limb-threatening ischemia in 52% and 80% were enrolled. All cases involved bilateral calcified occlusions, and 72% targeted the infrapopliteal artery segment. The average needle rendezvous time was 3.7 ± 2.0 min. Rendezvous-PIERCE was performed in 28% of cases. All cases achieved 100% technical and procedural success, with no procedure-related complications. The 30-day CDTLR rate was 8%, limited to below-the-knee lesions.ConclusionsNeedle rendezvous is a safe and effective technique for treating complex infrainguinal arterial occlusions, providing a viable alternative when conventional methods fail.

Multi-Batch Carrier-Based UAV Formation Rendezvous Method Based on Improved Sequential Convex Programming

The limitations of the existing catapults necessitate multiple batches of take-offs for carrier-based unmanned aerial vehicles (UAVs) to form a formation. Because of the differences in takeoff time and location of each batch of UAVs, ensuring the temporal and spatial consistency and rendezvous efficiency of the formation becomes crucial. Concerning the challenges mentioned above, a multi-batch formation rendezvous method based on improved sequential convex programming (SCP) is proposed. A reverse solution approach based on the multi-batch rendezvous process is developed. On this basis, a non-convex optimization problem is formulated considering the following constraints: UAV dynamics, collision avoidance, obstacle avoidance, and formation consistency. An SCP method that makes use of the trust region strategy is introduced to solve the problem efficiently. Due to the spatiotemporal coupling characteristics of the rendezvous process, an inappropriate initial solution for SCP will inevitably reduce the rendezvous efficiency. Thus, an initial solution tolerance mechanism is introduced to improve the SCP. This mechanism follows the idea of simulated annealing, allowing the SCP to search for better reference solutions in a wider space. By utilizing the initial solution tolerance SCP (IST-SCP), the multi-batch formation rendezvous algorithm is developed correspondingly. Simulation results are obtained to verify the effectiveness and adaptability of the proposed method. IST-SCP reduces the rendezvous time from poor initial solutions without significantly increasing the computing time.

Investigation of near-rectilinear halo orbit search and rescue using staging [formula omitted]/[formula omitted] Lyapunov and distant retrograde orbit families

Cislunar space is a region of growing interest with nations investing resources to cultivate long presence habitations on the lunar surface. With this increased attention and expansion of missions, both crewed and uncrewed, the likelihood of a mishap or a spacecraft becoming impaired and unable to continue its mission will also increase. The present research adds to the field of cislunar mission operations and trajectory analysis by investigating search and rescue (SAR) operations via rendezvous and proximity operations (RPO) with an impaired notional spacecraft located in a Near-Rectlinear Halo Orbit (NRHO). This research compares the response times of rescuer spacecraft located in sample distant retrograde orbits (DROs) and L1/L2 Lyapunov orbits for the timely far rendezvous with the impaired spacecraft located in the NRHO. This will simulate a variety of far rendezvous whereby the impaired spacecraft’s location within the NRHO and the rescuer spacecraft in the L1/L2 Lyapunov and DRO orbit families are varied. A series of minimum time optimal control problems are posed using the circular restricted three-body problem (CR3BP) dynamics, and pseudospectral methods are used to find solutions given an example maximum ΔV constraint of 3 km/s. The results reinforces our intuition that rendezvous time of flight (TOF) between orbits within the L1, L2, and DRO families and the targeted NRHO correlate with proximity to the NRHO, with the shortest far rendezvous times in each family found to be approximately 6 hours, 4.5 hours, and 10 hours respectively. The results further show that a constellation of two rescue spacecraft could be positioned within the three orbit families to achieve far rendezvous with the chosen NRHO in under one day.

Rapid generation of time-optimal rendezvous trajectory based on convex optimisation and DNN

Abstract The minimum flight time of spacecraft rendezvous is one of the fundamental indexes for mission design. This paper proposes a rapid trajectory planning method based on convex optimisation and deep neural network (DNN). The time-optimal trajectory planning problem is reconstructed into a double-layer optimisation framework, with the inner being a convex optimisation problem and the outer being a root-finding problem. The thrust properties corresponding to time-optimal control are analysed theoretically. A DNN-based rapid planning method (DNN-RPM) is put forward to improve computational efficiency, in which the trained DNN provides a high-quality initial guess for Newton’s method. The DNN-RPM is extended to search for the optimal entering angle of natural-motion circumnavigation orbit injection problem and the minimum reconfiguration time of spacecraft swarm. Numerical simulations show that the proposed method can improve the computational efficiency while ensuring the calculation accuracy.

Deterministic rendezvous in infinite trees

The rendezvous task calls for two mobile agents, starting from different nodes of a network modeled as a graph to meet at the same node. Agents have different labels which are integers from a set {1,…,L}. They wake up at possibly different times and move in synchronous rounds. In each round, an agent can either stay idle or move to an adjacent node. We consider deterministic rendezvous algorithms. The time of such an algorithm is the number of rounds since the wakeup of the earlier agent till the meeting. In most of the literature concerning rendezvous in graphs, the graph is finite and the time of rendezvous depends on its size. This approach is impractical for very large graphs and impossible for infinite graphs. For such graphs it is natural to design rendezvous algorithms whose time depends on the initial distance D between the agents. In this paper we adopt this approach and consider rendezvous in infinite trees. All our algorithms work in finite trees as well. Our main goal is to study the impact of orientation of a tree on the time of rendezvous.We first design a rendezvous algorithm working for unoriented regular trees, whose time is in O(z(D)log⁡L), where z(D) is the size of the ball of radius D, i.e., the number of nodes at distance at most D from a given node. The algorithm works for arbitrary delay between waking times of agents and does not require any initial information about parameters L or D. Its disadvantage is its complexity: z(D) is exponential in D for any degree d>2 of the tree. We prove that this high complexity is inevitable: Ω(z(D)) turns out to be a lower bound on rendezvous time in unoriented regular trees, even for simultaneous start and even when agents know L and D. Then we turn attention to oriented trees. While for arbitrary delay between waking times of agents the lower bound Ω(z(D)) still holds, for simultaneous start the time of rendezvous can be dramatically shortened. We show that if agents know either a polynomial upper bound on L or a linear upper bound on D, then rendezvous can be accomplished in oriented trees in time O(Dlog⁡L), which is optimal. If no such extra knowledge is available, a significant speedup is still possible: in this case we design an algorithm working in time O(D2+log2⁡L).

Global Trajectory Optimization of Multispacecraft Successive Rendezvous Using Multitree Search

This paper investigates the global optimization of multispacecraft successive rendezvous trajectories, which is divided here into three subproblems: target assignment, sequence optimization, and rendezvous time optimization. A method consisting of two novel algorithms is proposed to solve these subproblems. First, a multitree search framework is developed to assign multiple targets to each spacecraft and simultaneously optimize the rendezvous sequence for every single spacecraft. Specifically, a novel algorithm of local search combined with beam search is proposed. Second, this paper converts the rendezvous time optimization problem into a multistage decision problem. Based on a critical rendezvous-epoch-dependent characteristic found in this subproblem, the number of state variables is thereby reduced. A novel dual dynamic programming algorithm is proposed and combined with dynamic programming to solve for the globally optimal rendezvous epochs efficiently. Global optimality is guaranteed by Bellman’s principle of optimality, which is the first time in such a problem to our knowledge. The proposed method achieves state-of-the-art performance in several typical fuel-optimal scenarios of active debris removal. This open-sourced method is non-database-dependent and contains only one design stage, which is expected to be adopted in other successive rendezvous missions.

“Catheter Kissing” Technique to Recanalize Chronic Total Occlusions in Iliac Artery with Wire-Catheter Approach

PurposeTo describe a technique in which two 5-F curved catheters were utilized to facilitate the wire-catheter approach for recanalizing chronic total occlusions (CTOs) in the iliac arteries concurrently affecting the common iliac artery and external iliac artery. MethodsThis was a single-center retrospective analysis involving endovascular recanalization of 17 iliac artery CTOs in 15 patients (mean age: 73.66 years; all men) between January 2019 and October 2022 using the subintimal arterial flossing with antegrade–retrograde intervention technique. With antegrade and retrograde guidewires in the subintimal spaces of CTOs, the location where the two guidewires seemed to overlap was identified as the rendezvous point. Although the two guidewires appeared to be in close proximity, there was no evidence that the bidirectional subintimal channels were connected. If several initial attempts failed, two 5-F multipurpose catheters were introduced to the rendezvous point, followed by twisting, pulling, and pushing maneuvers until the tips of the catheters touched, indicating that the bidirectional subintimal channels were joined. A second wire rendezvous attempt was then employed to create a flossing-type guidewire. Outcome measurements included technical success, rendezvous points, complications, and procedure duration. ResultsAmong this cohort, 80.0% smoked and 66.7% had hypertension. In 11 limbs (64.7%), when initial wire rendezvous attempts failed, the "catheter kissing" technique was employed to successfully recanalize iliac artery CTOs, taking an average of 3.80 ± 1.64 minutes to complete the secondary wire rendezvous. The average length of CTOs was 111.06 ± 9.99 mm, with 7 (41.2%) and 8 (47.1%) cases exhibiting severe calcification and flush occlusion, respectively. The wire rendezvous point for all cases was in EIA and the average time for successful secondary wire rendezvous was 3.80 ± 1.64 minutes. All patients were treated with iliac artery stents. No statistically significant difference was observed between the puncture sites of the common femoral artery and superficial femoral artery in relation to failure of the primary wire rendezvous (p = 0.644). No in-hospital deaths or complications were associated with the procedure, including iliac artery rupture, distal embolization, or access site complications. ConclusionIn patients with extensive iliac artery CTOs, the "catheter kissing" technique may offer an effective and time-efficient recanalization approach, without requiring additional specialized devices. Importantly, the risk of complications remains unchanged even when employing a wire rendezvous in a challenging subintimal space.

New Construction of Asynchronous Channel Hopping Sequences in Cognitive Radio Networks.

The channel-hopping-based rendezvous is essential to alleviate the problem of under-utilization and scarcity of the spectrum in cognitive radio networks. It dynamically allows unlicensed secondary users to schedule rendezvous channels using the assigned hopping sequence to guarantee the self-organization property in a limited time. In this paper, we use the interleaving technique to cleverly construct a set of asynchronous channel-hopping sequences consisting of d sequences of period xN2 with flexible parameters, which can generate sequences of different lengths. By this advantage, the new designed CHSs can be used to adapt to the demands of various communication scenarios. Furthermore, we focus on the improved maximum-time-to-rendezvous and maximum-first-time-to-rendezvous performance of the new construction compared to the prior research at the same sequence length. The new channel-hopping sequences ensure that rendezvous occurs between any two sequences and the rendezvous times are random and unpredictable when using licensed channels under asynchronous access, although the full degree-of-rendezvous is not satisfied. Our simulation results show that the new construction is more balanced and unpredictable between the maximum-time-to-rendezvous and the mean and variance of time-to-rendezvous.

Anti-Jamming Low-Latency Channel Hopping Protocol for Cognitive Radio Networks

In order to increase channel usage efficiency, unlicensed users within a Cognitive Radio Network (CRN) are permitted to utilize channels that are not currently occupied by licensed users. However, ensuring communication between users in a CRN remains a challenge. To overcome this issue, a variety of channel hopping protocols have been developed. Time-invariant channel hopping protocols are vulnerable to attacks, so several channel hopping protocols that are resistant to jamming attacks have been proposed. In the majority of existing anti-jamming protocols, users create their channel hopping sequence using a channel hopping matrix, with the rendezvous probability between two users being determined by the structure of their respective channel hopping matrices. The channel hopping matrices designed by existing methods still have room for improvement. To overcome the difficulty of guaranteeing communication between any pair of users, while also providing protection against jamming attacks and minimizing the time to rendezvous (TTR) in a CRN, this paper presents the Anti-jamming Low-Latency channel hopping (ALL) protocol. This protocol allows a sender to adjust their channel hopping matrix structure to match that of the receiver, thereby improving the chances of successful rendezvous between users. Based on the simulation results, the ALL protocol performs better than the recently proposed practical solution, OLAA, by up to 33% in network throughput and 30% in TTR. On average, ALL outperforms OLAA by 25% in network throughput and 20% in TTR.

Active Debris Removal Mission Planning Method Based on Machine Learning

To prevent the proliferation of space debris and stabilize the space environment, active debris removal (ADR) has increasingly gained public concern. Considering the complexity of space operations and the viability of ADR missions, it would be necessary to schedule the ADR process in order to remove as much debris as possible. This paper presents an active debris removal mission planning problem, devoted to generate an optimal debris removal plan to guide the mission process. According to the problem characteristics, a two-layer time-dependent traveling salesman problem(TSP) mathematical model is established, involving the debris removal sequence planning and the transfer trajectory planning. Subsequently, two main novel methods based on machine learning are proposed for the ADR mission planning problem, including a deep neural networks(DNN)-based estimation method for approximating the optimal velocity increments of perturbed multiple-impulse rendezvous and an reinforcement learning(RL)-based method for optimizing the sequence of debris removal and rendezvous time. Experimental results of different simulation scenarios have verified the effectiveness and superiority of the proposed method, indicating the good performance for solving the active debris removal mission planning problem.

GTOC 11: Results from Tsinghua University and Shanghai Institute of Satellite Engineering

In this paper, the methods and results from Tsinghua University and Shanghai Institute of Satellite Engineering for the 11th Global Trajectory Optimization Competition (GTOC11) are presented. To deal with the complicated “Dyson Sphere” building problem, a three-stage procedure is conducted. First, the pre-analysis is performed to reduce search space. It is found that two-impulse maneuvers between asteroid flybys are near-optimal, the semi-major axis of the “Dyson Ring” should be better at 1.0–1.5 AU, and the larger arrival mass asteroids tend to be selected. Second, the globally optimal trajectory design problem is further divided into two sub-problems, the mothership trajectory design and the asteroid assignment to the “Dyson Ring” power stations. For the first problem, beam search is used to obtain numerous single mothership trajectories based on a pre-constructed flyby trajectory database of 3–8 asteroids. The overall trajectories and asteroids visited are obtained by selecting 10 mothership trajectories with a genetic algorithm. For the second problem, we build a database of optimal rendezvous times for all the 83,453 asteroids at different phase angles to reach power stations of different radii and phase angles, then a greedy algorithm is proposed to obtain the asteroid arrival schedule based on all the asteroids visited by motherships. Finally, local optimization of asteroid sequence and flyby epochs is conducted. The activation time adjustment in combination with indirect continuous-thrust trajectory optimization is used based on the global optimization result. In the final submission, motherships fly by 388 asteroids, and the minimum mass of twelve power stations reaches 94% of the theoretical upper bound, which is defined using the minimum-time orbital transfers with free initial and target phases.

Multiple GEO satellites on-orbit repairing mission planning using large neighborhood search-adaptive genetic algorithm

This paper proposes a novel large neighborhood search-adaptive genetic algorithm (LNS-AGA) for many-to-many on-orbit repairing mission planning of geosynchronous orbit (GEO) satellites with mission deadline constraint. In the many-to-many on-orbit repairing scenario, several servicing spacecrafts and target satellites are located in GEO orbits which have different inclination, right ascension of ascending node (RAAN) and true anomaly. Each servicing spacecraft need to rendezvous with target satellites to perform repairing missions under limited fuel. The mission objective is to find the optimal servicing sequence and orbit rendezvous time of each servicing spacecraft to minimize total Δv cost of all servicing spacecrafts with all target satellites repaired. Firstly, a time-dependent orbital rendezvous strategy is proposed, which can handle the mission deadline constraint. Besides, it is also cost-effective compared with the existing strategy. Based on this strategy, the many-to-many on-orbit repairing mission planning model can be simplified to an integer programming problem, which is established based on the vehicle routing problem with time windows (VRPTW) model. In order to efficiently find a feasible optimal solution under complicated constraints, a hybrid adaptive genetic algorithm combining the large neighborhood search procedure is designed. The operations of “destroy” and “repair” are used on the elite individuals in each generation of the genetic algorithm to enhance local search capabilities. Finally, simulation results under several different scenarios show the effectiveness and superiority of the presented algorithm and orbital rendezvous strategy.

Optimization of low-thrust multi-debris removal mission via an efficient approximation model of orbit rendezvous

An efficient iterative approximation model for low-thrust rendezvous in low-earth orbit is proposed to be applied in optimization of multi-debris removal missions. Based on an existing method for impulsive orbit rendezvous and a novel iteration process, the propellant cost and thrust time of a low-thrust rendezvous can be quickly evaluated. Moreover, another iterative method is also designed to help find the minimal transfer duration required for orbit rendezvous. Then, its application in the max-reward optimization of debris removal mission with a large-scale targets to be selected is studied. In the three-steps optimization including target selection, sequence optimization, and low-thrust trajectory optimization, the iterative approximation model is used to deal with the constraints and evaluate the objective functions more efficiently. The problem of the eighth Chinese trajectory optimization competition was used to test the performance, and a leading solution including 93 targets was found. Comparisons with previous results were made to prove the advantages of the method in this paper.

Energy-aware spectrum coordination with intelligent frequency-hopping for software defined networks

Software-defined Cognitive radio (CR) networking is considered a promising communication paradigm that can deliver huge spectrum opportunities for enabling massive deployment for wireless Internet-of-Things (IoT) applications and services. An important challenge in this domain is how to provide effective energy-efficient distributed spectrum coordination mechanisms (known as Spectrum Rendezvous), through which the CR IoT users can opportunistically coordinate their transmissions over the idle licensed frequency channels without relying on the existence of a dedicated common control channel (CCC). This paper proposes a novel frequency hopping (FH) distributed rendezvous mechanism for CR-capable IoT (CR-IoT) networks using grid-based quorum systems, referred to as adaptive grid-based quorum channel-hopping scheme. The proposed quorum-based scheme divides the time into equidistant cycle segments, referred to as quorum-based FH intervals. Each quorum interval consists of equal-duration beaconing intervals, each associated with a licensed channel. According to the proposed algorithm, each CR-IoT device randomly selects awake-sleep schedules based on the adopted quorum system structure. Any two devices can exchange their control information over the assigned channels of their common awake beaconing intervals. The proposed algorithm provides probabilistic guarantees on the successful rendezvous (RDV) between any two CR-IoT users within a single quorum-based FH interval (cycle) and dynamically adjusts the adopted QS structure based on the time-varying traffic load in the CR-IoT network such that the RDV probability and the expected average time to rendezvous improve with the least possible energy consumption. Compared to reference design schemes, the simulation results demonstrate that the proposed algorithm significantly increases the RDV probability, reduces the average rendezvous time, and reduces the energy consumption per successful RDV.

A Symbolic Programming Approach to the Rendezvous Search Problem

In this paper we solve the rendezvous problem on the line with markers that can be dropped at chosen times when the initial distance D between the players is known. In the case of one marker, the M_1 game, the marker is held by player II at the start of the game and, once dropped and found by player I, indicates in which direction player I must move. In the case of two markers, the M_2 game, each player holds one and the dropping times may differ. There is uncertainty regarding the problem initial configuration, and the goal is to minimize the expected rendezvous time that we call the rendezvous value (of the game) denoted R_1 and R_2 for the M_1 and M_2 games respectively. We present an algorithm that computes exactly the rendezvous value of the M_1 game as a function of the dropping time z, i.e. zmapsto R_1(z). Then we show that the function R_1(z) is locally an affine function and we compute the parameters of the local representations of R_1(z). Finally, the rendezvous value of the game R_1=min_z R_1(z) and the optimal dropping times can be determined with the expression of R_1(z). The same proceeding can be extended to apply to the problem M_2. Symbolic execution of programs is a classical technique of program testing in computer science, see King [1] for the pioneering work. In this work we adapt the symbolic execution technique to solve an optimization problem. To our knowledge this is the first time that this is attempted, in particular to deal with rendezvous problems.

Decentralized Multi-UAV Path Planning Based on Two-Layer Coordinative Framework for Formation Rendezvous

Unmanned aerial vehicle (UAV) formation rendezvous path planning problem is one of the important research topics in multiple UAV (multi-UAV) coordinated path planning. Aiming at solving low computational efficiency and poor scalability of the traditional multi-UAV path planning method, the decentralized multi-UAV path planning method suitable for obstacle environments is proposed. Firstly, the UAV rendezvous path planning problem with constraints such as the kinematics of UAVs and collision-free constraints is modeled as a non-convex optimal-control problem. To minimize formation rendezvous time and energy consumption, a two-layer coordinative framework is developed to solve this problem. In the coordination layer, relying only on the information of neighboring UAVs, each UAV in the decentralized communication graph negotiates the desired flight time using a consensus protocol to achieve coordination among UAVs. In the planning layer, the initial non-convex formation rendezvous path planning problem is decoupled into several sub-problems, which can be solved in parallel by path planners distributed on each UAV using sequential convex programming. Finally, numerical simulations are carried out to verify the effectiveness and scalability of the proposed method. The results show that this decentralized multi-UAV path planning method can handle the minimum-time rendezvous path planning problem and optimize the energy consumption in flight, and the computing time does not increase significantly with the enlargement of the UAV swarm. This decentralized framework scales well with the number of UAVs and can be applied for future urban flight and supplies delivery tasks.

Coordinated routing of electric commercial vehicles with intra-route recharging and en-route battery swapping

A primary challenge in goods distribution using Electric Commercial Vehicles (ECVs) pertains to tackling their limited driving range. This paper proposes a multi-faceted approach towards increasing the driving range of ECVs by coordinating the options of: (i) intra-route recharging at an intermediate Recharging Station (RS), with (ii) synchronised en-route battery swapping services performed by Battery Swapping Vans (BSVs) at a pre-planned rendezvous time and space. We introduce and solve a variant corresponding to an Electric Vehicle Routing Problem with Time Windows, RSs and Synchronised Mobile Battery Swapping (EVRPTW-RS-SMBS). In the proposed model, route planning is carried out synchronously for two interdependent fleets, i.e., ECVs and BSVs, which work in tandem to complete the delivery tasks. To address methodological complications arising from the simultaneous consideration of intra-route recharging at RSs and the synchronised battery swapping on-the-fly, the paper develops a pre-optimisation procedure based on a Non-Dominated Path Identification (NDPI) algorithm that is used in deriving a significantly strengthened path-based formulation of the problem, and an efficient dynamic programming based heuristic algorithm. To gain practical insights on the economic and environmental added value and viability of the proposed logistics model, we compare different scenarios for goods distribution using ECVs in urban and regional levels in London and Southeast England, respectively. A set of numerical experiments are further performed to demonstrate the efficiency of the proposed algorithms. Our results indicate significant cost and emissions savings and an opportunity for going beyond last mile local deliveries using ECVs with the proposed logistics model.

Search-and-rescue rendezvous

We consider a new type of asymmetric rendezvous search problem in which player II needs to give player I a ‘gift’ which can be in the form of information or material. The gift can either be transfered upon meeting, as in traditional rendezvous, or it can be dropped off by player II at a location he passes, in the hope it will be found by player I. The gift might be a water bottle for a traveller lost in the desert; a supply cache for Captain Scott in the Antarctic; or important information (left as a gift). The common aim of the two players is to minimize the time taken for I to either meet II or find the gift. We find optimal agent paths and drop off times when the search region is a line, the initial distance between the players is known and one or both of the players can leave gifts.A novel and important technique introduced in this paper is the use of families of linear programs to solve this and previous rendezvous problems. Previously, the approach was to guess the answer and then prove it was optimal. Our work has applications to other forms of rendezvous on the line: we can solve the symmetric version (players must use the same strategy) with two gifts and we show that there are no asymmetric solutions to this two gifts problem. We also solve the GiftStart problem, where the gift or gifts must be dropped at the start of the game. Furthermore, we can solve the Minmax version of the game where the objective function is to minimize the maximum rendezvous time. This problem admits variations where players have 0,1 or 2 gifts at disposal. In particular, we show that the classical Wait For Mommy strategy is optimal for this setting.

The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary

This paper studies the first passage times of a (reflected) Brownian motion with broken drift over a random boundary. The time-dependent Meyer–Tanaka formula allows us to obtain the formulas on the joint Laplace transform of the hitting time and hitting position. This paper extends the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry et al. (2004).

Computing Efficient Trajectories for Unmanned Air Vehicles (Dept.E)

Rapidly developments in the design and implementation of autonomous Unmanned Air Vehicles (UAVs) make the use of them in combat missions a real fact in the near future. One of the challenging problems yet to be solved is the real time planning of the optimal trajectory. Techniques used for robot motion planning are implemented for UAV e.g. cell decomposition, road maps and virtual forces. In these techniques a cost function consists of the threat cost and the length cost with priority factors and weighting quantities for both. The optimal trajectory (or timed path) is that producing the minimum cost function. Although this cost functional is composed of the two cost elements (length and threat) it conceals a source of error that produces optimal paths with high threat values i.e. not actually optimal and not safe. These results return to: a) the length cost dominates the effect on the cost function even with large weighting and priority for the threat cost. b) radar threats or probabilities of being detected by adverse radars are only considered, while threats of Surface to Air Missiles (SAMs) are not included in the threat function. c) weighting quantities given may be suitable for costs of some path edges and not suitable for other edges of the same path and other paths. In this paper a proposed algorithm to compute the real efficient path depending upon a proposed fitness function. The function gives a balanced domination for both length fitness and threat fitness. Besides, the threat on it consists of the two components: radars and SAMs. The algorithm autonomously computes the proper values of the weighting quantities that guide the fitness function towards the higher priority cost element in case of time constraint. It also gives the vehicle a necessary flexibility to adjust the pre-given priority factors in order to compute other optimal paths that fulfills a rendezvous time with the other team members.