15 research outputs found

    Robust safety zones for manipulators with uncertain dynamics in collaborative robotics

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    In this paper, an approach for computing online safety zones for collaborative robotics in a robust way, despite uncertain robot dynamics, is proposed. The strategy implements the speed and separation monitoring paradigm, and considers human and robot enclosed in bounding volumes. The human-robot collaboration is monitored by a supervisory controller that guides the robot to stop along a path-consistent trajectory in case of collision danger between human and robot. The size of the robot safety zone is minimized online according to the stop time of the manipulator, and the uncertain robot dynamics is considered using interval arithmetic to ensure compliance with the joint torques limits even in case of imperfect knowledge of the dynamic model parameters. The results verify the effectiveness of the proposed approach, and evaluate the influence of dynamics variations on human-robot collaboration

    An Autonomous Path Planning Method for Unmanned Aerial Vehicle based on A Tangent Intersection and Target Guidance Strategy

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    Unmanned aerial vehicle (UAV) path planning enables UAVs to avoid obstacles and reach the target efficiently. To generate high-quality paths without obstacle collision for UAVs, this paper proposes a novel autonomous path planning algorithm based on a tangent intersection and target guidance strategy (APPATT). Guided by a target, the elliptic tangent graph method is used to generate two sub-paths, one of which is selected based on heuristic rules when confronting an obstacle. The UAV flies along the selected sub-path and repeatedly adjusts its flight path to avoid obstacles through this way until the collision-free path extends to the target. Considering the UAV kinematic constraints, the cubic B-spline curve is employed to smooth the waypoints for obtaining a feasible path. Compared with A*, PRM, RRT and VFH, the experimental results show that APPATT can generate the shortest collision-free path within 0.05 seconds for each instance under static environments. Moreover, compared with VFH and RRTRW, APPATT can generate satisfactory collision-free paths under uncertain environments in a nearly real-time manner. It is worth noting that APPATT has the capability of escaping from simple traps within a reasonable time

    Modeling Framework for Identification and Analysis of Key Metrics for Trajectory Energy Management of Electric Aircraft

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    Presented at AIAA AVIATION Forum, August 2-6, 2021, VIRTUAL EVENTTo prepare for the upcoming entry into service of electric and hybrid-electric aircraft, regulators may have to update or develop new regulations and standards to ensure safe operations of these new vehicles. To ensure public acceptance, these vehicles need to demonstrate an equivalent level of safety consistent with existing regulations. However, the ability to fly in different modes (forward flight, vertical flight) and the different powertrain elements may require significant changes to regulations to ensure that an insightful representation of the usable energy is provided to flight crews. This requires an understanding of the major operational differences between conventional and electric aircraft, and how these differences impact the trajectories a vehicle can fly. For instance, there is no simple analog to fuel gauges for measuring the extractable energy available on board electric aircraft, as energy related metrics can vary with a range of variables, such as component temperatures, battery health, and environmental conditions. It is thus more complex for flight crews to gauge in real-time how much usable energy is available and to figure out which trajectories are feasible with respect to both energy and power. To assess the feasibility of trajectories and quantify the adequacy of novel energy tracking metrics and methodologies, a trajectory energy management simulation environment is implemented allowing the simulation of various energy metrics across a range of vehicles and missions. This allows decision makers and regulators to assess the importance of these metrics for safe operation across a wide variety of missions. The impact of ambient air temperature, battery state of health, and initial battery, motor, and inverter temperatures are assessed for a typical flight mission. It is concluded that state of health, ambient temperature, and initial battery temperature all had significant impacts on the final state of charge and amount of extractable energy. Additionally, at high ambient temperatures and in aggressive climbs, motor temperature limits and inverter temperature limits can sometimes be reached, further complicating the assessment of what can be done with the amount of energy stored on board. Proper management of these constraints is therefore crucial for optimizing trajectories with respect to energy metrics. Future work is proposed regarding further expansion of the framework simulating aircraft with vertical takeoff and landing capability, and flight-dynamics algorithms that will enable simulation of optimal energy mission profiles

    A generalized laser simulator algorithm for optimal path planning in constraints environment

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    Path planning plays a vital role in autonomous mobile robot navigation, and it has thus become one of the most studied areas in robotics. Path planning refers to a robot's search for a collision-free and optimal path from a start point to a predefined goal position in a given environment. This research focuses on developing a novel path planning algorithm, called Generalized Laser Simulator (GLS), to solve the path planning problem of mobile robots in a constrained environment. This approach allows finding the path for a mobile robot while avoiding obstacles, searching for a goal, considering some constraints and finding an optimal path during the robot movement in both known and unknown environments. The feasible path is determined between the start and goal positions by generating a wave of points in all directions towards the goal point with adhering to constraints. A simulation study employing the proposed approach is applied to the grid map settings to determine a collision-free path from the start to goal positions. First, the grid mapping of the robot's workspace environment is constructed, and then the borders of the workspace environment are detected based on the new proposed function. This function guides the robot to move toward the desired goal. Two concepts have been implemented to find the best candidate point to move next: minimum distance to goal and maximum index distance to the boundary, integrated by negative probability to sort out the most preferred point for the robot trajectory determination. In order to construct an optimal collision-free path, an optimization step was included to find out the minimum distance within the candidate points that have been determined by GLS while adhering to particular constraint's rules and avoiding obstacles. The proposed algorithm will switch its working pattern based on the goal minimum and boundary maximum index distances. For static obstacle avoidance, the boundaries of the obstacle(s) are considered borders of the environment. However, the algorithm detects obstacles as a new border in dynamic obstacles once it occurs in front of the GLS waves. The proposed method has been tested in several test environments with different degrees of complexity. Twenty different arbitrary environments are categorized into four: Simple, complex, narrow, and maze, with five test environments in each. The results demonstrated that the proposed method could generate an optimal collision-free path. Moreover, the proposed algorithm result are compared to some common algorithms such as the A* algorithm, Probabilistic Road Map, RRT, Bi-directional RRT, and Laser Simulator algorithm to demonstrate its effectiveness. The suggested algorithm outperforms the competition in terms of improving path cost, smoothness, and search time. A statistical test was used to demonstrate the efficiency of the proposed algorithm over the compared methods. The GLS is 7.8 and 5.5 times faster than A* and LS, respectively, generating a path 1.2 and 1.5 times shorter than A* and LS. The mean value of the path cost achieved by the proposed approach is 4% and 15% lower than PRM and RRT, respectively. The mean path cost generated by the LS algorithm, on the other hand, is 14% higher than that generated by the PRM. Finally, to verify the performance of the developed method for generating a collision-free path, experimental studies were carried out using an existing WMR platform in labs and roads. The experimental work investigates complete autonomous WMR path planning in the lab and road environments using live video streaming. The local maps were built using data from live video streaming s by real-time image processing to detect the segments of the lab and road environments. The image processing includes several operations to apply GLS on the prepared local map. The proposed algorithm generates the path within the prepared local map to find the path between start-to-goal positions to avoid obstacles and adhere to constraints. The experimental test shows that the proposed method can generate the shortest path and best smooth trajectory from start to goal points in comparison with the laser simulator

    ๋‹ค์–‘ํ•œ ๊ต๋ž€ ์‹œ๋‚˜๋ฆฌ์˜ค๋ฅผ ์ด์šฉํ•œ GNSS ์ˆ˜์‹ ๊ธฐ ์„ฑ๋Šฅ ๋ถ„์„์— ๋Œ€ํ•œ ์—ฐ๊ตฌ

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    ํ•™์œ„๋…ผ๋ฌธ(๋ฐ•์‚ฌ)--์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› :๊ณต๊ณผ๋Œ€ํ•™ ๊ธฐ๊ณ„ํ•ญ๊ณต๊ณตํ•™๋ถ€,2020. 2. ๊ธฐ์ฐฝ๋ˆ.The security and safety aspects of global navigation satellite systems have been receiving significant attention from researchers and the general public, because the use of GNSS has been increasing in modern society. In this situation, the importance of GNSS safety and security is also increasing. The most dangerous type of interference is a spoofing because if the receiver captures a spoofing signal, the navigation solution can be controlled by the spoofer. In this paper, I analyzed the characteristics of the main spoofing parameters that determines the success or failure of spoofing process when the spoofing signal is injected into the receiver. I also proposed a CCEE. It determines the spoofing result according to the various spoofing parameter. Also the correlation between spoofing parameters could be explained by estimating the boundary value and line using CCEE. In addition, spoofing success and failure could be distinguished in the spoofing parameter space using CCEE results. When the covert capture is performed at the receiver, the two correlation peaks of authentic and covert capture signals are generated on the code domain. The relative velocity (Doppler difference value) of the two signal peaks determines the time of total spoofing process. In general, the timing at which the DLL tracking lock point is switched from the authentic signal to the spoofing signal is different according to the visible satellite. This raises the value of WSSE. In order to minimize this, the spoofing should be performed in a short time by determining the optimal sweep direction. In a 3D situation, triangles are defined using a particular visible satellites, and the circumcenter direction of the triangle on the victim becomes the optimal direction, and the relative speed of the authentic and the covert capture signal for the visible satellite be maximized on the optimal covert capture direction. To simulate the proposed methods, we defined the covet capture scenarios and generated the IF data to simulate the intended scenarios. Then, using the corresponding IF data, signal processing was performed through SDR. Through this, it was confirmed that the spoofing is successfully performed as intended scenarios through the optimal spoofing parameters generated through CCEE, and the covert capture process time is noticeably minimized through the optimal sweep direction.GNSS๋Š” ์ ์  ํ™œ์šฉ๋ฒ”์œ„๊ฐ€ ํ™•์žฅ๋˜๊ณ  ์žˆ๊ณ , ํ˜„์žฌ๋Š” ๋Œ€์ฒด๋ถˆ๊ฐ€๋Šฅํ•œ ์‹œ์Šคํ…œ์ด ๋˜์—ˆ๋‹ค. ์ด๋Ÿฐ ์ƒํ™ฉ์—์„œ GNSS์˜ ์•ˆ์ „ ๋ฐ ๋ณด์•ˆ์˜ ์ค‘์š”์„ฑ ๋˜ํ•œ ํฌ๊ฒŒ ์ฆ๊ฐ€ํ•˜๊ณ  ์žˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” GNSS์˜ ๋ณด์•ˆ์— ๊ฐ€์žฅ ์œ„ํ˜‘์ด ๋˜๋Š” ๊ธฐ๋งŒ์— ๋Œ€ํ•ด์„œ, ๊ธฐ๋งŒ ์‹ ํ˜ธ๊ฐ€ ์ˆ˜์‹ ๊ธฐ์— ์ฃผ์ž…๋˜์—ˆ์„ ๋•Œ ์ˆ˜์‹ ๊ธฐ์˜ ACF๊ฐ€ ์–ด๋–ป๊ฒŒ ๋ณ€ํ™”๋˜์–ด ๊ฐ€๋ฉฐ ๊ธฐ๋งŒ ๊ณต๊ฒฉ์„ ๊ฒฐ์ •ํ•˜๋Š” ์ฃผ๋œ ๊ธฐ๋งŒํŒŒ๋ผ๋ฏธํ„ฐ๋“ค์˜ ํŠน์ง•์— ๋Œ€ํ•ด์„œ ๋ถ„์„์„ ์ง„ํ–‰ํ•˜์˜€๋‹ค. ๊ทธ๋ฆฌ๊ณ  ๊ธฐ๋งŒ ์‹ ํ˜ธ์— ๋”ฐ๋ฅธ ๊ธฐ๋งŒ ๊ฒฐ๊ณผ๋ฅผ ๊ฒฐ์ •ํ•˜๋Š” CCEE๋ฅผ ์ œ์•ˆํ•˜๊ณ , ์ด๋ฅผ ํ†ตํ•ด์„œ ๊ธฐ๋งŒํŒŒ๋ผ๋ฏธํ„ฐ๋“ค์˜ ์ƒ๊ด€๊ด€๊ณ„์— ๋Œ€ํ•ด์„œ ๋ถ„์„ํ•˜์˜€๋‹ค. ๊ธฐ์กด์—๋Š” ๋ฌด์ˆ˜ํžˆ ๋ฐ˜๋ณต๋œ ๊ณ„์‚ฐ์„ ํ†ตํ•ด์„œ ํŒ๋‹จ ๊ฐ€๋Šฅํ•œ ๊ธฐ๋งŒ ๊ฒฐ๊ณผ๋ฅผ CCEE๋ฅผ ํ†ตํ•ด ํ•œ๋ฒˆ์˜ ๊ณ„์‚ฐ์œผ๋กœ ๊ฒฐ๊ณผ๋ฅผ ํ™•์ธํ•˜๋„๋ก ํ•˜์˜€๋‹ค. ๋˜ํ•œ CCEE๋ฅผ ์ด์šฉํ•˜์—ฌ ๊ฒฝ๊ณ„ ๊ฐ’๊ณผ ๊ฒฝ๊ณ„ ๋ผ์ธ์„ ์ •์˜ํ•จ์œผ๋กœ์จ, ๊ธฐ๋งŒํŒŒ๋ผ๋ฏธํ„ฐ ๊ณต๊ฐ„์—์„œ ๊ธฐ๋งŒ ์„ฑ๊ณต๊ณผ ์‹คํŒจ๋ฅผ ๊ตฌ๋ถ„ํ•  ์ˆ˜ ์žˆ์Œ์ด ํ™•์ธ๋˜์—ˆ๋‹ค. ์ˆ˜์‹ ๊ธฐ์—์„œ ๊ธฐ๋งŒ์ด ์ˆ˜ํ–‰๋  ๋•Œ, ์ฝ”๋“œ๋„๋ฉ”์ธ์ƒ์—์„œ replica์™€ cross correlation์— ์˜ํ•œ ์›์‹ ํ˜ธ์™€ ๊ธฐ๋งŒ์‹ ํ˜ธ ๊ฐ๊ฐ์˜ correlation peak๊ฐ€ ์ƒ์„ฑ๋œ๋‹ค. ๋‘ ์‹ ํ˜ธ peak์˜ ์ƒ๋Œ€์†๋„๊ฐ€ ๊ธฐ๋งŒ์ด ์ˆ˜ํ–‰๋˜๋Š” ์‹œ๊ฐ„์„ ๊ฒฐ์ •ํ•œ๋‹ค. ์ผ๋ฐ˜์ ์œผ๋กœ ๊ธฐ๋งŒ์ด ์ˆ˜ํ–‰๋˜๋Š” ๋™์•ˆ, ๊ฐ ์ฑ„๋„๊ฐ„ DLL tracking lock ์ง€์ ์ด ์›์‹ ํ˜ธ์—์„œ ๊ธฐ๋งŒ์‹ ํ˜ธ๋กœ ์ „ํ™˜๋˜๋Š” ์‹œ์ ์ด ๋‹ค๋ฅด๋‹ค. ์ด๋กœ ์ธํ•ด์„œ WSSE์˜ ๊ฐ’์ด ์ƒ์Šนํ•˜๊ฒŒ ๋œ๋‹ค. ์ด๋ฅผ ์ตœ์†Œํ™”ํ•˜๊ธฐ ์œ„ํ•ด์„œ, ์ตœ์  ๊ธฐ๋งŒ sweep ๋ฐฉํ–ฅ์„ ๊ฒฐ์ •ํ•จ์œผ๋กœ์จ ๋น ๋ฅธ ์‹œ๊ฐ„์— ๊ธฐ๋งŒ์„ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ์Œ์„ ํ™•์ธํ•˜์˜€๋‹ค. 3D ์ƒํ™ฉ์—์„œ ํŠน์ • ๊ฐ€์‹œ์œ„์„ฑ๋ฅผ ์ด์šฉํ•˜์—ฌ ์‚ผ๊ฐํ˜•์„ ์ •์˜ํ•˜๊ณ , ํ•ด๋‹น ์‚ผ๊ฐํ˜•์˜ ์™ธ์‹ฌ ๋ฐฉํ–ฅ์ด ์ตœ์  ๋ฐฉํ–ฅ์ด ๋˜๋ฉฐ, ํ•ด๋‹น ๋ฐฉํ–ฅ์ด ๊ธฐ๋งŒ ์ˆ˜ํ–‰์ด ๊ฐ€์žฅ ๋Šฆ๊ฒŒ ๋˜๋Š” ๊ฐ€์‹œ์œ„์„ฑ์— ๋Œ€ํ•œ ์›์‹ ํ˜ธ์™€ ๊ธฐ๋งŒ์‹ ํ˜ธ์˜ ์ƒ๋Œ€์†๋„๊ฐ€ ์ตœ๋Œ€๊ฐ€ ๋˜๋Š” ๋ฐฉํ–ฅ์ž„์„ ํ™•์ธํ•˜์˜€๋‹ค. ์ œ์•ˆ๋œ ๋ฐฉ๋ฒ•๋“ค์„ ๋ชจ์‚ฌํ•˜๊ธฐ ์œ„ํ•ด์„œ, ๊ธฐ๋งŒ์‹œ๋‚˜๋ฆฌ์˜ค๋ฅผ ์ •์˜ํ•˜๊ณ , ํ•ด๋‹น ๊ธฐ๋งŒ์‹œ๋‚˜๋ฆฌ์˜ค๋ฅผ ๋ชจ์‚ฌํ•˜๋Š” IF data๋ฅผ ์ƒ์„ฑํ•˜์˜€๋‹ค. ๊ทธ๋ฆฌ๊ณ , ํ•ด๋‹น IF data๋ฅผ ์ด์šฉํ•˜์—ฌ, SDR์„ ํ†ตํ•ด์„œ ์‹ ํ˜ธ ์ฒ˜๋ฆฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€๋‹ค. ์ด๋ฅผ ํ†ตํ•ด, CCEE๋ฅผ ์ ์šฉํ•˜์—ฌ ์ƒ์„ฑํ•œ ์ตœ์  ๊ธฐ๋งŒํŒŒ๋ผ๋ฏธํ„ฐ๋กœ ๊ธฐ๋งŒ์ด ์˜๋„๋œ ๋ฐ๋กœ ์ˆ˜ํ–‰์ด ๋˜๋ฉฐ, optimal ๋ฐฉํ–ฅ์„ ํ†ตํ•ด ๊ธฐ๋งŒ์ˆ˜ํ–‰์‹œ๊ฐ„์ด ์ตœ์†Œํ™” ๋จ์„ ํ™•์ธํ•˜์˜€๋‹ค.Chapter 1. Introduction 1 1.1. Research Motivation ๏ผ‘ 1.2. Related research ๏ผ’ 1.3. Outline of the Dissertation ๏ผ” 1.4. Contributions 5 Chapter 2. Background ๏ผ— 2.1. GPS receiver fundamental ๏ผ— 2.1.1. GPS signal structure ๏ผ— 2.1.2. Signal processing structure of GPS receiver ๏ผ™ 2.1.3. Signal acquisition ๏ผ‘๏ผ 2.1.4. Signal tracking ๏ผ‘๏ผ‘ 2.1.5. Navigation Message Decoding ๏ผ‘๏ผ” 2.1.6. Pseudorange model and range calculation ๏ผ‘๏ผ– 2.2. GNSS interferences and attack strategies ๏ผ‘๏ผ™ 2.2.1. Types of GNSS interferences ๏ผ‘๏ผ™ 2.2.2. Interference attack strategies ๏ผ’๏ผ‘ Chapter 3. Covert Capture Effectiveness Equation ๏ผ’๏ผ– 3.1. Authentic and spoofing signal ACF model ๏ผ’๏ผ– 3.2. Spoofing scenario simulation using ACF model ๏ผ“๏ผ 3.3. Development of spoofing process equation ๏ผ“๏ผ“ 3.3.1. conventional approach for tau calculation ๏ผ“๏ผ“ 3.3.2. proposed approach for ฯ„ calculation ๏ผ“๏ผ” 3.3.3. Spoofing attack success or failure criteria ๏ผ“๏ผ— 3.3.4. Derivation of SPE ๏ผ”๏ผ” 3.4. Analysis of CCEE simulation results ๏ผ”๏ผ™ 3.4.1. CCEE performance analysis ๏ผ”๏ผ™ 3.4.2. Determination of boundary line and surface using SPE ๏ผ•๏ผ“ Chapter 4. Optimal sweep direction of covert capture signal ๏ผ•๏ผ˜ 4.1. Maximum Doppler difference value ๏ผ•๏ผ˜ 4.2. Optimal covert capture direction in 2D case ๏ผ–๏ผ’ 4.3. Optimal covert capture direction in 3D case ๏ผ–๏ผ˜ 4.4. Optimal covert capture direction using optimization method ๏ผ—๏ผ‘ Chapter 5. Covert capture simulation using software defined receiver ๏ผ—๏ผ“ 5.1. Implementation of GNSS measurement and IF data generation simulator ๏ผ—๏ผ“ 5.1.1. Pseudorange model ๏ผ—๏ผ“ 5.1.2. Simulator structure ๏ผ—๏ผ” 5.1.3. Signal amplitude calculation in spoofing scenario ๏ผ—๏ผ• 5.2. CCEE simulation in SDR ๏ผ˜๏ผ‘ 5.2.1. Compensation value calculation for covert capture ๏ผ˜๏ผ” 5.2.2. Compensation value calculation for covert capture ๏ผ˜๏ผ• 5.3. Optimal covert capture direction simulation in SDR ๏ผ™๏ผ’ Chapter 6. Changing the user's trajectory using covert capture signal ๏ผ™๏ผ• Chapter 7. Conclusions and future works ๏ผ‘๏ผ๏ผ’ 7.1. Conclusions ๏ผ‘๏ผ๏ผ’ 7.2. Future works ๏ผ‘๏ผ๏ผ“ Capture 8. Reference ๏ผ‘๏ผ๏ผ”Docto

    Middleware and Architecture for Advanced Applications of Cyber-physical Systems

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    In this thesis, we address issues related to middleware, architecture and applications of cyber-physical systems. The first problem we address is the cross-layer design of cyber-physical systems to cope with interactions between the cyber layer and the physical layer in a dynamic environment. We propose a bi-directional middleware that allows the optimal utilization of the common resources for the benefit of either or both the layers in order to obtain overall system performance. The case study of network connectivity preservation in a vehicular formation illustrates how this approach can be applied to a particular situation where the network connectivity drives the application layer. Next we address another aspect of cross-layer impact: the problem that arises when network performance, in this case delay performance, affects control system performance. We propose a two-pronged approach involving a flexible adaptive model identification algorithm with outlier rejection, which in turn uses an adaptive system model to detect and reject outliers, thus shielding the estimation algorithm and thereby improving reliability. We experimentally demonstrate that the outlier rejection approach which intercepts and filters the data, combined with simultaneous model adaptation, can result in improved performance of Model Predictive Control in the vehicular testbed. Then we turn to two advanced applications of cyber-physical systems. First, we address the problem of security of cyber-physical systems. We consider the context of an intelligent transportation system in which a malicious sensor node manipulates the position data of one of the autonomous cars to deviate from a safe trajectory and collide with other cars. In order to secure the safety of such systems where sensor measurements are compromised, we employ the procedure of โ€œdynamic watermarkingโ€. This procedure enables an honest node in the control loop to detect the existence of a malicious node within the feedback loop. We demonstrate in the testbed that dynamic watermarking can indeed protect cars against collisions even in the presence of sensor attacks. The second application of cyber-physical systems that we consider is cyber-manufacturing which is an origami-type laser-based custom manufacturing machine employing folding and cutting of sheet material to manufacture 3D objects. We have developed such a system for use in a laser-based autonomous custom manufacturing machine equipped with real-time sensing and control. The basic elements in the architecture are a laser processing machine, a sensing system to estimate the state of the workpiece, a control system determining control inputs for a laser system based on the estimated data, a robotic arm manipulating the workpiece in the work space, and middleware supporting the communication among the systems. We demonstrate automated 3D laser cutting and bending to fabricate a 3D product as an experimental result. Lastly, we address the problem of traffic management of an unmanned aerial system. In an effort to improve the performance of the traffic management for unmanned aircrafts, we propose a probability-based collision resolution algorithm. The proposed algorithm analyzes the planned trajectories to calculate their collision probabilities, and modifies individual drone starting times to reduce the probability of collision, while attempting to preserve high performance. Our simulation results demonstrate that the proposed algorithm improves the performance of the drone traffic management by guaranteeing high safety with low modification of the starting times

    A Scalable Safety Critical Control Framework for Nonlinear Systems

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    There are two main approaches to safety-critical control. The first one relies on computation of control invariant sets and is presented in the first part of this work. The second approach draws from the topic of optimal control and relies on the ability to realize Model-Predictive-Controllers online to guarantee the safety of a system. In the second approach, safety is ensured at a planning stage by solving the control problem subject for some explicitly defined constraints on the state and control input. Both approaches have distinct advantages but also major drawbacks that hinder their practical effectiveness, namely scalability for the first one and computational complexity for the second. We therefore present an approach that draws from the advantages of both approaches to deliver efficient and scalable methods of ensuring safety for nonlinear dynamical systems. In particular, we show that identifying a backup control law that stabilizes the system is in fact sufficient to exploit some of the set-invariance conditions presented in the first part of this work. Indeed, one only needs to be able to numerically integrate the closed-loop dynamics of the system over a finite horizon under this backup law to compute all the information necessary for evaluating the regulation map and enforcing safety. The effect of relaxing the stabilization requirements of the backup law is also studied, and weaker but more practical safety guarantees are brought forward. We then explore the relationship between the optimality of the backup law and how conservative the resulting safety filter is. Finally, methods of selecting a safe input with varying levels of trade-off between conservatism and computational complexity are proposed and illustrated on multiple robotic systems, namely: a two-wheeled inverted pendulum (Segway), an industrial manipulator, a quadrotor, and a lower body exoskeleton
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