Kinematic Restrictions Research Articles

Soft theorems in matrix theory

We show that the Banks-Fischler-Shenker-Susskind matrix model for M-theory obeys the leading and subleading soft theorems expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.

Assistance by adaptative damping on a complex bimanual task in laparoscopic surgery.

Laparoscopic surgery has improved outcomes in abdominal surgery, but presents kinematic restrictions for surgeons. Robotic comanipulation with adaptative damping has been investigated in simple laparoscopic tasks. The present protocol aimed to determine the contribution of adaptive damping in complex bimanual tasks approaching clinical setting. Fourteen residents in general surgery performed three exercises, and for each three repetitions without (classic repetitions) and three with robotic assistance (robotic repetitions) in a randomised order. The exercises chosen were trajectory, modified Pea on a Peg and intracorporeal suture. Task performance, gesture performance, workload and impression were measured. Also, a semi-directed interview was performed to collect the participants' feeling about companipulated robots and their potential application in clinical practice. Adaptative damping assistance did not impact task performance, but allowed an economy of movement in the non-dominant hand during suture exercise (distance 916 ± 500mm in classic vs. 563 ± 261mm in robotic, p < 0.001). Perceived workload (p = 0.12) and user's impression were not different between classic and robotic repetitions, except novelty (p < 0.001). Participants' interviews revealed their interest for the robotic devices, particularly the gravity compensation, and were ready to use the adaptative damping provided an intermittent use, for example to dissect dangerous areas. Adaptative damping applied by comanipulated robots does not influence the performance of the task, but improves the performance of the gesture itself, particularly for the non-dominant hand, and during the realisation of a complex task like suturing. For residents in digestive surgery, this assistance does increase workload, and they would use this help in the operating room under certain conditions.

A study of the K+→ π0e+νγ decay

A sample of 1.3 × 105K+ → π0e+νγ candidates with less than 1% background was collected by the NA62 experiment at the CERN SPS in 2017–2018. Branching fraction measurements are obtained at percent relative precision in three restricted kinematic regions, improving on existing results by a factor larger than two. An asymmetry, possibly related to T-violation, is investigated with no evidence observed within the achieved precision.

Using Inverse Dynamics Technique in Planning Autonomous Vehicle Speed Mode Considering Physical Constraints

The study aims at improving the technique of planning the autonomous vehicles’ (AV) speed mode based on a kinematic model with physical restrictions. A mathematical model relates the derivatives of kinematic parameters with ones of the trajectory’s curvature. The inverse approach uses an expanded vehicle model considering the distribution of vertical reactions, wheels’ longitudinal reactions according to a drive type, and lateral forces ensuring motion stability. For analysis of the drive type, four options are proposed: front-wheel drive (FWD), rear-wheel drive (RWD), permanent engaged all-wheel drive (AWD), and 4-wheel drive with torque vectoring (4WD-TV). The optimization model is also built by the inverse scheme. The longitudinal speed’s higher derivatives are modeled by the finite element (FE) functions with nodal unknowns. The sequential integrations ensure the optimality and smoothness of the third derivative. The kinematic restrictions are supplemented by the tire-road critical slip states. Sequential quadratic programming (SQP) and the Gaussian N-point scheme for quadrature integration are used to minimize the objective function. The simulation results show a significant difference in the mode forecasts between four types of AV drives at the same initial conditions. This technique allows redistributing the traction forces strictly according to the wheels’ adhesion potentials and increases the optimization performance by about 40% compared to using the kinematic model based on the same technique without physical constrains.

Research on path planning of autonomous vehicle based on RRT algorithm of Q-learning and obstacle distribution

PurposeThe goal of this research is to develop a dynamic step path planning algorithm based on the rapidly exploring random tree (RRT) algorithm that combines Q-learning with the Gaussian distribution of obstacles. A route for autonomous vehicles may be swiftly created using this algorithm.Design/methodology/approachThe path planning issue is divided into three key steps by the authors. First, the tree expansion is sped up by the dynamic step size using a combination of Q-learning and the Gaussian distribution of obstacles. The invalid nodes are then removed from the initially created pathways using bidirectional pruning. B-splines are then employed to smooth the predicted pathways.FindingsThe algorithm is validated using simulations on straight and curved highways, respectively. The results show that the approach can provide a smooth, safe route that complies with vehicle motion laws.Originality/valueAn improved RRT algorithm based on Q-learning and obstacle Gaussian distribution (QGD-RRT) is proposed for the path planning of self-driving vehicles. Unlike previous methods, the authors use Q-learning to steer the tree's development direction. After that, the step size is dynamically altered following the density of the obstacle distribution to produce the initial path rapidly and cut down on planning time even further. In the aim to provide a smooth and secure path that complies with the vehicle kinematic and dynamical restrictions, the path is lastly optimized using an enhanced bidirectional pruning technique.

The language of knee alignment : updated definitions and considerations for reporting outcomes in total knee arthroplasty.

Orthopaedic surgeons are currently faced with an overwhelming number of choices surrounding total knee arthroplasty (TKA), not only with the latest technologies and prostheses, but also fundamental decisions on alignment philosophies. From 'mechanical' to 'adjusted mechanical' to 'restricted kinematic' to 'unrestricted kinematic' - and how constitutional alignment relates to these - there is potential for ambiguity when thinking about and discussing such concepts. This annotation summarizes the various alignment strategies currently employed in TKA. It provides a clear framework and consistent language that will assist surgeons to compare confidently and contrast the concepts, while also discussing the latest opinions about alignment in TKA. Finally, it provides suggestions for applying consistent nomenclature to future research, especially as we explore the implications of 3D alignment patterns on patient outcomes.Cite this article: Bone Joint J2023;105-B(2):102-108.

Measurement of Hand Joint Angle Using Inertial-Based Motion Capture System

The inertial sensor motion capture system has significant advantages over the classical optical motion capture system, including its high versatility, portability, and affordability. However, its accuracy is over one order of magnitude lower than the optical system. The measurement error of the finger joint angle is mainly due to sensor drift and misalignment of sensor to finger segment. In this article, we propose a method that includes both orientation estimation and calibration for accurate joint angle estimation. Specifically, at first, the accuracy of the sensor orientation is greatly improved using the square root cubature Kalman filter (SRCKF) to fuse the magnetic and inertial measurement units (MIMUs) data. Second, the kinematic restrictions of the finger joints are used for initial and in-process calibration to achieve sensor-to-segment (StoS) calibration throughout the process. Finally, the difference between the orientation of the two adjacent segments is the joint angle. Experiments show that our proposed system improves joint measurement accuracy compared with the existing inertial sensor-based systems. Evaluation of ten participants showed that the average root mean square error (RMSE) of finger joint measurements is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.5^{\circ }(\pm 4.0^{\circ })$ </tex-math></inline-formula> . Our proposed system provides accurate information in measuring hand joint angles and quantifying hand movement function in clinical practice.

Adaptative damping assistance in bimanual laparoscopic surgery.

Laparoscopic surgery has demonstrated various advantages for the patients' care, but also presents some difficulties for the surgeons, such as kinematic restrictions. Robotic comanipulation, in which control of instruments is shared between the robot and the surgeon, can provide adaptative damping assistance which allows stabilisation of movements. The objective of the present study was to determine the contribution of this assistance on a bimanual laparoscopic task. Adaptative damping was studied on Peg Transfer task, performed by eighteen surgery-naive subjects. This exercise was repeated seven times without (Classic repetitions) and seven times with comanipulated robots (Robot repetitions), in a randomised order. We measured task performance, using Peg Transfer score; gesture performance, using hand oscillations and travelled distance; eye-tracking movements as an indicator of emergence of expertise. Participants' perceived workload was assessed by NASA TLX questionnaire, and difference in impression between the two conditions by UEQ questionnaire. Adaptative damping improved gesture performance (oscillations F(1,17) = 23.473, p < 0.001, η2 = 0.580), with a statistically significant simple effect on the tool oscillation for both non-dominant (p < 0.001) and dominant hands (p = 0.005), without influencing task performance (mean Peg Transfer score t(17) = 0.920, p = 0.382, d = 0.29), but deteriorating eye-tracking movements associated with emergence of expertise (mean fixation rate per second F(1,17) = 6.318, p = 0.022, η2 = 0.271), at the cost of a high perceived workload (NASA TLX score 59.78/100). Assistance by adaptative damping applied by comanipulated robots improved gesture performance during a laparoscopic bimanual task, without impacting task's performance without allowing the emergence of comportments associated with an expertise, and at the cost of a high perceived workload. Further research should investigate this assistance on more precise and clinical tasks performed by professionals.

The impact of different alignment strategies on bone cuts for neutral knee phenotypes in total knee arthroplasty

PurposeThe purpose of this study was to simulate and visualise the influence of the alignment strategy on bone resection in neutral knee phenotypes. It was hypothesised that different amounts of bone resection would be required depending on the alignment strategy chosen. The hypothesis was that by visualising the corresponding bone cuts, it would be possible to assess which of the different alignment strategies required the least change to the soft tissues for the chosen phenotype but still ensured acceptable component alignment and could, therefore, be considered the most ideal alignment strategy.MethodsSimulations of the different alignment strategies (mechanical, anatomical, restricted kinematic and unrestricted kinematic) regarding their bone resections were performed on four common exemplary neutral knee phenotypes. NEUHKA0° VARFMA 90° VALTMA90°, NEUHKA0° NEUFMA 93° NEUTMA87°, NEUHKA0° VALFMA 96° NEUTMA87° and NEUHKA0° VALFMA 99° VARTMA84°. The phenotype system used categorises knees based on overall limb alignment (i.e. hip knee angle) but also considers joint line obliquity (i.e. TKA and FMA) and has been used globally since its introduction in 2019. These simulations are based on long leg weightbearing radiographs. It is assumed that a change of 1° in the alignment of the joint line corresponds to correspond to 1 mm of distal condyle offset.ResultsIn the most common neutral phenotype NEUHKA0° NEUFMA 93° NEUTMA87°, with a prevalence of 30%, bone cuts remain below 4 mm regardless of alignment strategy. The greatest changes in the obliquity of the joint line can be expected for the mechanical alignment of the phenotype NEUHKA0° VALFMA 99° VARTMA84° where the medial tibia is raised by 6 mm and the lateral femur is shifted distally by 9 mm. In contrast, the NEUHKA0° VARFMA 90° VALTMA90° phenotype requires no change in joint line obliquity if the mechanical alignment strategy is used.ConclusionIllustrations of alignment strategies help the treating surgeon to estimate the postoperative joint line obliquity. When considering the alignment strategy, it seems reasonable to prefer a strategy where the joint line obliquity is changed as little as possible. Although for the most common neutral knee phenotype the choice of alignment strategy seems to be of negligible importance, in general, even for neutral phenotypes, large differences in bone cuts can be observed depending on the choice of alignment strategy.

The coronal alignment technique impacts deviation from native knee anatomy after total knee arthroplasty.

The aim of this study was to analyze and quantify the changes in native coronal alignment of a population of TKA patients according to different alignment goals. Five hundred and twenty TKAs were analyzed. The following angles were measured using an image-free navigation system prior to prosthetic implantation: medial femorotibial mechanical angle without stress and with maximum manual stress to reduce the deformity, medial distal femoral mechanical angle, medial proximal tibial mechanical angle. The native angles were derived from the osteoarthritic knee angles using a validated correction technique, and the overall, femoral and tibial coronal phenotypes were defined. Five different coronal alignment techniques were simulated: mechanical (MA), restricted mechanical (RMA), anatomical (AA), kinematic (KA) and restricted kinematic (RKA). The overall, femoral and tibial coronal phenotypes were compared before and after TKA. The primary endpoint was the binary criterion of whether or not TKA restored the natural overall phenotype. Secondary endpoints were the binary criteria of whether or not the natural femoral and tibial phenotypes were restored by TKA. The rates of restored and non restored phenotypes were compared with a Chi-square test at a 0.05 level of significance, with post hoc tests between all pairs of techniques at a 0.01 level of significance. The overall phenotype was restored significantly differently by the five alignment techniques: 15% for MA, 23% for RMA, 2% for AA, 100% for KA and 79% for RKA (p < 0.001). There was a significant difference between each of the technique pairs (p < 0.01 to p < 0.001), except for the mechanical alignment-restricted mechanical alignment pair. The femoral phenotype was restored significantly differently by the five alignment techniques: 37% for MA, 58% for RMA, 19% for AA, 100% for KA and 85% for RKA (p < 0.001). The tibial phenotype was restored significantly differently by the five alignment techniques: 36% for MA, 36% for RMA, 17% for AA, 100% for KA and 88% for RKA (p < 0.001). There was a significant difference between each pair of techniques for both femoral and tibial phenotypes (p < 0.01 to p < 0.001). Except for the kinematic alignment technique, the various alignment techniques induce significant changes in the pre-arthritic anatomy of the TKA patient. The surgeon must be aware of these modifications. The clinical relevance of this alteration still needs to be defined. III.

Assessment of the effect of a total contact cast on lower limb kinematics and joint loading

BackgroundTotal contact casts (TCCs) are used to immobilize and unload the foot and ankle for the rehabilitation of ankle fractures and for the management of diabetic foot complications. The kinematic restrictions imposed by TCCs to the foot and ankle also change knee and hip kinematics, however, these changes have not been quantified before. High joint loading is associated with discomfort and increased risk for injuries. To assess joint loading, the effect of the muscle forces acting on each joint must also be considered. This challenge can be overcome with the help of musculoskeletal modelling. Research questionHow does a TCC affect lower extremity joint loading? MethodsTwelve healthy participants performed gait trials with and without a TCC. Kinematic and kinetic recordings served as input to subject-specific musculoskeletal models that enabled the computation of joint angles and loading. Cast-leg interaction was modelled by means of reaction forces between a rigid, zero-mass cast segment and the segments of the lower extremity. Resultsand Significance: Reduced ankle, knee and hip range of motion was observed for the TCC condition. Statistical parametric mapping indicated decreased hip abduction and flexion moments during initial contact with the TCC. The anterior knee force was significantly decreased during the mid and terminal stance and the second peak of the compressive knee force was significantly reduced for the TCC. As expected, the TCC resulted in significantly reduced ankle loading. SignificanceThis study is the first to quantify the effect of a TCC on lower limb joint loading. Its results demonstrate the efficiency of a TCC in unloading the ankle joint complex without increasing the peak loads on knee and hip. Future studies should investigate whether the observed knee and hip kinematic and kinetic differences could lead to discomfort.

Neutral Mechanical Alignment Alters the Native Distal Femoral Joint Line: A Virtual Three-Dimensional Planning Total Knee Arthroplasty Study

BackgroundAlternative alignment concepts have garnered great interest in an effort to improve patient satisfaction following primary total knee arthroplasty (TKA). The purpose of this study is to determine variation or deviation from an individual’s native joint line in primary TKA using neutral mechanical versus a restricted kinematic technique. MethodsAn institutional review board–approved prospective cohort study was performed evaluating the effect of neutral mechanical alignment (nMA) versus a restricted kinematic alignment (rKA) on the native joint line in 100 consecutive patients undergoing primary TKA. Using preoperative computed tomography and intraoperative 3-dimensional software, 2 virtual preoperative plans were created: nMA and rKA. Templated bone resections were recorded. Change in joint line was calculated using known implant planar thickness and planned bone resection. ResultsnMA yielded significantly greater deviation from the patient’s native joint line along the lateral compartment of the knee (lateral distal femoral condyle, lateral posterior femoral condyle, lateral tibial resection). With nMA, the lateral distal femoral joint line was distalized by a mean 4.3 versus 2.6 mm using rKA technique (P < .001). In rKA, >60% of knees had <3 mm of deviation from the native lateral posterior femoral offset, whereas in nMA, >95% of knees had ≥3 mm change in the lateral posterior femoral condylar offset. ConclusionnMA-TKA resulted in statistically larger joint line deviations compared to rKA-TKA, most notably along the lateral distal femoral condyle joint line. Further analysis is needed to determine the clinical consequences of joint line deviation from the native anatomy using nMA as the target for primary TKA.

On Fast Jerk-Continuous Motion Functions with Higher-Order Kinematic Restrictions for Online Trajectory Generation

In robotics and automated manufacturing, motion functions for parts of machines need to be designed. Many proposals for the shape of such functions can be found in the literature. Very often, time efficiency is a major criterion for evaluating the suitability for a given task. If there are higher precision requirements, the reduction in vibration also plays a major role. In this case, motion functions should have a continuous jerk function but still be as fast as possible within the limits of kinematic restrictions. The currently available motion designs all include assumptions that facilitate the computation but are unnecessary and lead to slower functions. In this contribution, we drop these assumptions and provide an algorithm for computing a jerk-continuous fifteen segment profile with arbitrary initial and final velocities where given kinematic restrictions are met. We proceed by going systematically through the design space using the concept of a varying intermediate velocity and identify critical velocities and jerks where one has to switch models. The systematic approach guarantees that all possible situations are covered. We implemented and validated the model using a huge number of random configurations in Matlab, and we show that the algorithm is fast enough for online trajectory generation. Examples illustrate the improvement in time efficiency compared to existing approaches for a wide range of configurations where the maximum velocity is not held over a period of time. We conclude that faster motion functions are possible at the price of an increase in complexity, yet which is still manageable.

Geometrically constrained path planning for robotic grasping with Differential Evolution and Fast Marching Square

AbstractThis paper presents a new approach for geometrically constrained path planning applied to the field of robotic grasping. The method proposed in this paper is based on the Fast Marching Square (FM $\, ^2$ ) and a path calculation approach based on an optimization evolutionary filter named Differential Evolution (DE). The geometric restrictions caused by the link lengths of the kinematic chain composed by the robot arm and hand are introduced in the path calculation phase. This phase uses both the funnel potential of the surroundings created with FM $\, ^2$ and the kinematic constraints of the robot as cost functions to be minimized by the evolutionary filter. The use of an optimization filter allows for a near-optimal solution that satisfies the kinematic restrictions, while preserving the characteristics of a path computed with FM $\, ^2$ . The proposed method is tested in a simulation using a robot composed by a mobile base with two arms.

Kinematic restriction method for tensegrity structures

The use of tensegrity structures in robotics has been studied in recent years thanks to their properties of light weight, efficient distribution of forces and the possibility of applying control methods for the active shape reconfiguration, with crawling and rolling as examples. The structural composition of tensegrities, particularly the use of tensile elements, results in the presence of infinitesimal mechanisms. These affine motions have been considered for the development of control strategies that follow the manifold of stable positions described by these mechanisms. However, in robotic applications, the presence of rigid body motions can cause undesired effects, such as tensegrity structures flipping over. The form finding methods available in literature consider only the statics of tensegrities and most dynamic models work assume free-standing structures, while few consider fixed structures but do not deepen into the process of removing the rigid body motions. In this paper, the formulation of the equilibrium equations of tensegrity structures is reviewed, to describe the presence of the affine motions in the vector spaces of the equilibrium matrix. A simplified method for removing rigid body motions from the equilibrium equations is detailed, and the effect on the set of affine motions is explained. To verify the validity of this process, two numerical examples are given, including a single unit and a two stage tensegrity structures.

Three-gluon vertex in Landau-gauge from quenched-lattice QCD in general kinematics

We report on a novel and extensive lattice QCD analysis for the three-gluon vertex from quenched lattice-QCD simulations. Using standard Wilson action, we have computed the three-gluon vertex beyond the usual kinematic restriction to the symmetric (q2 = r2 = p2) and soft-gluon (p = 0) cases where it depends on a single momentum scale. The so-dubbed bisectoral case (r2 = q2 ≠ p2), where the transversely projected vertex can be cast in terms of three independent tensors, have been the object of a recent exhaustive scrutiny [1], also shown in this communication. Herein, beyond this special case, results for kinematic configurations with three different squared momenta are also presented. All data considered, the lattice estimate of the three-gluon vertex exhibits a clear dominance of the tree-level tensor form factor.

How large is the diffractive contribution to inclusive dijet photoproduction in ultraperipheral collisions at the LHC?

Using next-to-leading order (NLO) perturbative QCD, we calculate the diffractive contribution to inclusive dijet photoproduction in Pb-Pb ultraperipheral collisions (UPCs) at the LHC and find that it does not exceed $5-10$% in small-$x_A$ bins in the ATLAS kinematics at $\sqrt{s_{NN}}=5.02$ TeV. Its smallness is a result of the restricted kinematics ($p_{T1} > 20$ GeV and $x_A > 0.001$), the large nuclear suppression of nuclear diffractive parton distribution functions predicted in the leading twist model of nuclear shadowing, and additional suppression due to QCD factorization breaking in diffraction. At the same time, using looser $p_T$ cuts, e.g., $p_{T1} > 10$ GeV and $p_{T i\neq 1} > 5-7$ GeV, we find that $(d\sigma_{\rm diff}/dx_A)/(d\sigma_{\rm inc}/dx_A)$ can reach $10-20$% at $x \approx 5 \times 10^{-4}$. Also, applying our framework to proton-proton UPCs at $\sqrt{s_{NN}}=13$ TeV, we find that the ratio of the diffractive and inclusive cross sections of dijet photoproduction $(d\sigma_{\rm diff}/dx_p)/(d\sigma_{\rm inc}/dx_p)$ is as large as $10-15$% for $x_p \sim 5 \times 10^{-4}$. An account of the contribution of Pomeron-Pomeron scattering, which is not included in our analysis, should make this ratio somewhat larger.

Restricted Kinematics in Children With Autism in the Execution of Complex Oscillatory Arm Movements.

Restricted and repetitive behavior is a core symptom of autism spectrum disorder (ASD) characterized by features of restrictedness, repetition, rigidity, and invariance. Few studies have investigated how restrictedness is manifested in motor behavior. This study aimed to address this question by instructing participants to perform the utmost complex movement. Twenty children with ASD and 23 children with typical development (TD) performed one-dimensional, left-right arm oscillations by demonstrating varying amplitudes and frequencies. The entropy of amplitude and velocity was calculated as an index of kinematic complexity. Results showed that the velocity entropy, but not the amplitude entropy, was significantly lower in ASD than in TD (p < 0.01), suggesting restricted kinematics. Further analysis demonstrated that a significantly higher proportion of the velocity values was allocated at a low-speed level in the children with ASD (p < 0.01). A qualitative comparison of the complex movement with movement at preferred frequency suggested that the children with ASD might be less likely to shift away from the preferred movement. However, our study can be improved in terms of recruiting a larger sample of participants, measuring the level of motivation, and collecting both complex and preferred movements of the same participant.

Patient satisfaction following total knee arthroplasty using restricted kinematic alignment.

Alternative alignment concepts, including kinematic and restricted kinematic, have been introduced to help improve clinical outcomes following total knee arthroplasty (TKA). The purpose of this study was to evaluate the clinical results, along with patient satisfaction, following TKA using the concept of restricted kinematic alignment. A total of 121 consecutive TKAs performed between 11 February 2018 to 11 June 2019 with preoperative varus deformity were reviewed at minimum one-year follow-up. Three knees were excluded due to severe preoperative varus deformity greater than 15°, and a further three due to requiring revision surgery, leaving 109 patients and 115 knees to undergo primary TKA using the concept of restricted kinematic alignment with advanced technology. Patients were stratified into three groups based on the preoperative limb varus deformity: Group A with 1° to 5° varus (43 knees); Group B between 6° and 10° varus (56 knees); and Group C with varus greater than 10° (16 knees). This study group was compared with a matched cohort of 115 TKAs and 115 patients using a neutral mechanical alignment target with manual instruments performed from 24 October 2016 to 14 January 2019. Mean overall patient satisfaction for the entire cohort was 4.7 (SE 0.1) on a 5-point Likert scale, with 93% being either very satisfied or satisfied compared with a Likert of 4.3 and patient satisfaction of 81% in the mechanical alignment group (p < 0.001 and p < 0.006 respectively). At mean follow-up of 17 months (11 to 27), the mean overall Likert, Knee Injury and Osteoarthritis Outcome Score for Joint Replacement, Western Ontario and McMaster Universities Osteoarthritis Index, Forgotten Joint Score, and Knee Society Knee and Function Scores were significantly better in the kinematic group than in the neutral mechanical alignment group. The most common complication in both groups was contracture requiring manipulation under anaesthesia, involving seven knees (6.1%) in the kinematic group and nine knees (7.8%) in the mechanical alignment group. With the advent of advanced technology, and the ability to obtain accurate bone cuts, the target limb alignment, and soft-tissue balance within millimetres, using a restricted kinematic alignment concept demonstrated excellent patient satisfaction following primary TKA. Longer-term analysis is required as to the durability of this method. Cite this article: Bone Joint J2021;103-B(6 Supple A):59-66.

Online flight path planning with flight time constraints for fixed-wing UAVs in dynamic environments

PurposeA major challenge for mission planning of aircraft is to generate flight paths in highly dynamic environments. This paper presents a new approach for online flight path planning with flight time constraints for fixed-wing UAVs. The flight paths must take into account the kinematic restrictions of the vehicle and be collision-free with terrain, obstacles and no-fly areas. Moreover, the flight paths are subject to time constraints such as predetermined time of arrival at the target or arrival within a specified time interval.Design/methodology/approachThe proposed flight path planning algorithm is an evolution of the well-known RRT* algorithm. It uses three-dimensional Dubins paths to reflect the flight capabilities of the air vehicle. Requirements for the flight time are realized by skillfully concatenating two rapidly exploring random trees rooted in the start and target point, respectively.FindingsThe approach allows to consider static obstacles, obstacles which might pop up unexpectedly, as well as moving obstacles. Targets might be static or moving with constantly changing course. Even a change of the target during flight, a change of the target approach direction or a change of the requested time of arrival is included.Originality/valueThe capability of the flight path algorithm is demonstrated by simulation results. Response times of fractions of a second qualify the algorithm for real-time applications in highly dynamic scenarios.