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Watt Linkage–Based Legged Deployable Landing Mechanism for Reusable Launch Vehicle: Principle, Prototype Design, and Experimental Validation
Abstract
The reusable launch vehicle (RLV) presents a new avenue for reducing cost of space transportation. The landing mechanism, which provides landing support and impact absorption, is a vital component of the RLV at final stage of recovery. This study proposes a novel legged deployable landing mechanism (LDLM) for RLV. The Watt-II six-bar mechanism is adopted to obtain the preferred configuration via the application of the linkage variation approach. To endow the proposed LDLM with advantages of large landing support region, lightweight, and reasonable linkage internal forces, a multi-objective optimization paradigm is developed. Furthermore, the optimal scale parameters for guiding the LDLM prototype design is obtained numerically using the non-dominated sorting genetic algorithm-II (NSGA-II) evolutionary algorithm. A fully-functional scaled RLV prototype is developed by integrating the gravity-governed deploying scheme to facilitate unfolding action to avoid full-range actuation, a dual-backup locking mechanism to enhance reliability of structure stiffening as fully deployed, and a shock absorber (SA) with multistage honeycomb to offer reliable shock absorbing performance. The experimental results demonstrate that the proposed LDLM is capable of providing rapid and smooth deployment (duration less than 1.5 s) with mild posture disturbance to the cabin (yaw and pitch fluctuations less than 6°). In addition, it provides satisfactory impact attenuation (acceleration peak less than 10g) in the 0.2 m freefall test, which makes the proposed LDLM a potential alternative for developing future RLV archetype.
... Subsequent research has sporadically tapped into the possibilities of NSGA in leg linkage design. For instance, studies by Xu et al., (2023) and later by Yu et al. (2023) have indicated the algorithm's utility in achieving optimal joint coordination, which is integral to effective leg linkage [23,24]. More recently, the research by Zhang and Cai (2023) extended these principles to more complex multi-legged robotic systems, demonstrating NSGA-II's adaptability in diverse locomotive configurations [25]. ...
... Subsequent research has sporadically tapped into the possibilities of NSGA in leg linkage design. For instance, studies by Xu et al., (2023) and later by Yu et al. (2023) have indicated the algorithm's utility in achieving optimal joint coordination, which is integral to effective leg linkage [23,24]. More recently, the research by Zhang and Cai (2023) extended these principles to more complex multi-legged robotic systems, demonstrating NSGA-II's adaptability in diverse locomotive configurations [25]. ...
In the ever-evolving domain of robotic locomotion, leg linkage design emerges not just as an intricate engineering puzzle, but also as a decisive element in realizing optimal horizontal propulsion. The research meticulously interrogates this pivotal concern, endeavoring to harmonize multiple design objectives that traditionally exist in tension. Leveraging the robust computational prowess of the Non-dominated Sorting Genetic Algorithm (NSGA) for multiobjective optimization, this study orchestrates a deliberate foray into the expansive and complex design space. The overarching aim is not merely to pinpoint a singular, universal design zenith, but to painstakingly chart a continuum of Pareto-optimal solutions, thereby accommodating the myriad, often contradictory, imperatives that animate robotic design—from the quest for energy efficiency to the pursuit of agility, speed, and robust structural integrity. This methodology yields a rich tapestry of insights: notable among them is the discernible predilection of specific linkage configurations towards distinct performance outcomes. While certain geometries resonate more profoundly with rapid, fluid motion, others evince a marked inclination towards stability or frugal energy consumption. By dissecting these intricate relationships, and presenting them within a structured framework, this study contributes profoundly to the literature, offering both theoretical depth and pragmatic design templates to the robotics community. This synergistic marriage of computational algorithms with nuanced design challenges holds the promise to significantly recalibrate and enhance contemporary paradigms in leg linkage design for horizontally propelling robots. This study marks a significant advancement in robotic locomotion by employing the Non-dominated Sorting Genetic Algorithm (NSGA) for the first time in the optimization of leg linkage design for walking robots, providing a more nuanced understanding of the balance between structural integrity, energy efficiency, and propulsion agility. Our research elucidates a spectrum of Pareto-optimal solutions, a novel approach that offers a comprehensive understanding of the trade-offs involved in leg linkage design. Specifically, the optimized designs achieved an improvement in propulsion efficiency by reducing the approximation error to less than 0.006, and enhancing force transmission angles to over 25 degrees. These experimental results validate the practical applicability of these designs, demonstrating a balance of improved efficiency and stability, thereby setting a new benchmark for leg linkage design in walking robots. The findings underscore the potential of NSGA in robotic design, offering a robust framework for future advancements in the field.
... Witte et al. [9] presented a high-fidelity numerical simulation to analyze the lander touchdown dynamics in the presence of planetary terrain features. Yu et al. [10] proposed a novel legged deployable landing mechanism for RLV, which has proved to be a potential alternative for developing future landing mechanisms after being systematically evaluated and improved. Thies [4] developed a rigid model of a legged landing mechanism with nonlinear spring characteristics, which can be used to analyze different complex landing scenarios for a stable landing to reach the parking position. ...
In this work, a vertical landing mechanism of a reusable launch vehicle (RLV) is investigated using a flexible–rigid coupled dynamics model. The presented model takes into account the four-legged landing mechanism and the main body cabin. Flexibilities of the main components in the vertical landing mechanism are considered. The hydro-pneumatic spring force and thrust aftereffect caused by the sequential deactivation of the engine are introduced separately. Several simulation cases are selected to analyze the loads acting on the landing mechanism and the dynamics behavior of the whole RLV system. Simulation results show that considering flexibility in the landing mechanism is critical for dynamics analysis under various initial conditions. The adopted RLV design is capable of achieving stable landings under specified initial velocity and attitude conditions, demonstrating its feasibility for engineering applications. Moreover, the hydro-pneumatic spring plays a crucial role in absorbing the impact of the initial landing leg, ensuring a smoother landing experience and minimizing potential damage to the vehicle.
... This allows the foundation to oscillate without transferring energy to the structure above. Similarly, the stabilizing feet are designed with a triple pendulum isolator system to reduce oscillations [12], and the part of the foot in contact with the surface is anchored with the deeper layers of regolith for stability (see Fig. 10). ...
Establishing a permanent human presence on the Moon is a crucial step towards becoming an interplanetary species and enabling further exploration of the Solar System. This paper presents a comprehensive design approach for the initial modules that will form the foundation of a lunar colony at the South Pole, accommodating the first crew of four astronauts. Our multidisciplinary team conducted an extensive study of historical literature and state-of-the-art human habitat designs to develop an innovative proposal tailored for lunar colonization. The proposed outpost is designed to evolve through distinct phases, utilizing four different module types: a Vertical Surface Habitat for the living environment, two distinct Horizontal Modules serving various functions such as laboratories, storage, and greenhouse, and an evolvable Node module that facilitates grid expansion and connection of additional modules. Leveraging 3D modelling tools, architectural design principles, and immersive virtual reality simulations, we consolidated our final design for the layout, structure, and interior configurations of these modules. The paper emphasizes the importance of incorporating hybrid modules from the outset of lunar colonization efforts. This hybrid approach, combining rigid and inflatable components, offers remarkable gains in terms of mass and volume optimization, which are critical factors for the initial human settlement on the Moon's surface. Through digital evaluation systems and trade studies, we demonstrate the significance of standardization and reconfigurability of internal usable volume within the modules. The hybrid design allows for efficient utilization of space while accommodating the evolving needs of the colony as it grows and expands over time. This work underscores the importance of hybrid module design for lunar colonization following the Artemis missions. Future research should focus on further optimizing the mass of these modules through advanced materials and construction techniques, as well as exploring additional configuration possibilities for the interiors of the horizontal modules to support a wider range of activities. The design presented in this paper is the result of a collaborative effort with the Sasakawa
... Inspiration for the leg system was taken from a 2022-published paper featuring a Watt-II 6-bar linkage-based LDLM (Legged Deployable Landing Mechanism.) used on the Falcon 9 11 , with adaptations made to the dimensions to raise the height to 4m, permitting the pressurized rover to dock underneath the habitat. This leg system also allows for variation in the habitat's landing profile and provides tolerance as the habitat becomes loaded with outfitted goods, experiences moonquakes 12 , and is mated to other modules. ...
The evolution to sustainable habitation on the Lunar surface presents an array of challenges, from the technical, administrative, and operational. A phased approach to using increasingly sustainable elements includes three types of habitats-class 1, 2, and 3. Class 1 habitations include rigid and unchanging element structure. Class 2 habitations include deployable or expandable elements on the lunar surface. Class 3 habitats incorporate in-situ resource utilization (ISRU) to bolster or form the outpost's element(s). The proposed outpost will primarily utilize a hybrid of class 1 and 2 habitat types. The team's approach intends to show an evolution of habitat types on the lunar surface by defining scientific objectives, research, and technical drivers, with inspiration from existing habitats in low-Earth orbit. The project will utilize habitat designs the team created considering sustainability, standardization, expandability, and relocatability. Focus was given to the concept of operations of a habitat design that is applicable across several targeted landing sites. The team further considered risk mitigations to ensure the best chance of crew survival, science survival, and mission success.
... However, the aluminum honeycomb can be used only once due to its energy dissipation mechanism, i.e., the plastic dissipation of metallic material. In terms of reusable energy absorption structures, metal rubber, hydraulic, mechanical, and electrical/magnetic rheological are the most common types [13][14][15]. At this point, energy absorption structures of the aforementioned types can serve as reusable landing gears. ...
The footpad structure of a deep space exploration lander is a critical system that makes the initial contact with the ground, and thereby plays a crucial role in determining the stability and energy absorption characteristics during the impact process. The conventional footpad is typically designed with an aluminum honeycomb structure that dissipates energy through plastic deformation. Nevertheless, its effectiveness in providing cushioning and energy absorption becomes significantly compromised when the structure is crushed, rendering it unusable for reusable landers in the future. This study presents a methodology for designing and evaluating structural energy absorption systems incorporating recoverable strain constraints of shape memory alloys (SMA). The topological configuration of the energy absorbing structure is derived using an equivalent static load method (ESL), and three lightweight footpad designs featuring honeycomb-like Ni-Ti shape memory alloys structures and having variable stiffness skins are proposed. To verify the accuracy of the numerical modelling, a honeycomb-like structure subjected to compression load is modeled and then compared with experimental results. Moreover, the influence of the configurations and thickness distribution of the proposed structures on their energy absorption performance is comprehensively evaluated using finite element simulations. The results demonstrate that the proposed design approach effectively regulates the strain threshold to maintain the SMA within the constraint of maximum recoverable strain, resulting in a structural energy absorption capacity of 362 J/kg with a crushing force efficiency greater than 63%.
... Zhang et al. [4] , based on the one degree of freedom (DOF) six-bars leg mechanism as the research object, carried out configuration design by studying the motion chain diagram and obtained the synthesis method of the one DOF jumping leg mechanism. Yu et al. [5] designed a novel mechanism for launch vehicles by using multi-objective optimization based on Watt six-bar units. ...
In this paper, three Watt six-bar units are proposed to construct a loop connection mechanism (Loop-Watt mechanism) with a single degree of freedom (DOF) through the loop connection of rotating joints, and the constructed mechanism can complete the turnover motion. First of all, by analyzing the characteristics of the Watt six-bars unit and the theme idea of loop connection, the concrete method of loop connection is proposed, and the construction method of the Loop-Watt mechanism (LW-M) is obtained. Secondly, the DOF, motion forms, and motion characteristics of the Loop-Watt mechanism are analyzed, and its motion modes are obtained. Finally, the correctness of the analysis results is verified by establishing a 3D model in SolidWorks software. The Loop-Watt mechanism constructed in this paper is expected to have important application prospects in sealing mechanisms and large deployable mechanisms.
... In the literature [11], two landing modes, shutdownbefore-touchdown and shutdown-at-touchdown, were proposed in consideration of the two conditions of the Mars lander's engines during landing, and the landing stability and impact on the collision under these two modes were analyzed. Therefore, considering the coupling effect of collision and buffering is an important factor to simulate the landing process of a vehicle with the inverted-triangle landing gear [12]. ...
In order to investigate the landing process of a vertical landing reusable vehicle, a dynamic model with a complex nonlinear dissipative element is established based on the discrete impulse step approach, which includes a three-dimensional multi-impact model considering friction and material compliance, and a multistage aluminum honeycomb theoretical model. The normal two-stiffness spring model is adopted in the foot–ground impact model, two motion patterns (stick and slip) are considered on the tangential plane and the structural changes caused by buffering behavior are included, and the energy conversion during the impact follows the law of conservation of energy. The state transition method is used to solve the dynamic stability convergence problem of the vehicle under the coupling effect of impact and buffering deformation in the primary impulse space. Landing experiments on a scaled physical reusable vehicle prototype are conducted to demonstrate that the theoretical results exhibit good agreement with the experimental data.
Unmanned helicopters equipped with adaptive landing gear will dramatically extend their application especially in dealing with challenging terrains. This study presents a novel cable-driven legged landing gear (CLG) with differential transmission for unmanned helicopters in complex landing environments. To obtain the preferred configuration of the legged mechanism, a multi-objective optimization framework for the CLG is constructed by concurrently considering terrain adaptability, landing stability and reasonable linkage of internal forces. The non-dominated sorting genetic algorithm II is employed to numerically acquire the optimal scale parameters that guide the mechanical design of the CLG. An unmanned helicopter prototype equipped with the devised CLG is developed with key performance assessment. Experimental results show that the devised CLG can provide energy-efficient support over uneven terrains (totally driven torque demand less than 0.1 N m) in quasi-static landing tests, and favorable terrain adaptability (posture fluctuation of the fuselage less than ±1°) in unknown slope landing tests. These exhibited merits give the proposed CLG the potential to enhance the landing performance of future aircraft in extreme environments.
Landing gear system is a key part of the implementation of reusable vertical takeoff and vertical landing launch vehicle, where its buffing performance is directly related to the vehicle whether it can land safely or stably. According to the reusable launch vehicle general scheme, outrigger landing legs are designed, and the hydraulic absorber is used for the landing gear system. Meanwhile, a scaling principle prototype of landing gear system is developed, and the landing impact test is carried out. A dynamic simulation model of the landing vehicle has been set up, researching the influence of parameters, such as the horizontal velocity, initial inclination, surface friction coefficient, and pitch angular velocity on the landing performance. Four kinds of extreme conditions are identified, and dynamic response characteristics of landing system under each extreme condition are conducted. The simulation results are in good agreement with the experimental data. The buffing performance of the vehicle meets the design requirements, which provides a reference for the design of landing gear system of the vehicle.
Based on oleo-honeycomb dampers, a 6-DOF vertical soft landing dynamic model for reusable launch vehicle considering landing strut flexibility is constructed. In order to better analyze the lateral deflection and friction force of the “cantilever beam” type landing strut, a new model for strut is incorporated. Static analysis is first performed based on the rotation angle compatibility equations to attain the equivalent inertia moment. Then the strut lateral vibration model and friction force model are obtained by simplifying it as viscoelastic beam with a tip mass. After that, the ADAMS models are established to perform the comparison and verification analysis of the 6-DOF dynamic model. The results show that the results of 6-DOF dynamic model can approximately approach to the results of rigid-flex coupling model established in ADAMS. Furthermore, the research of the influence of assembly gap between cylinders and bearings, bearing’s elastic modulus, friction coefficient and initial overlapping length on the vehicle landing performance is carried out. The results show that each parameter has different influence on the landing performance, and a reasonable selection of these parameters accordingly enables a higher landing performance.
This paper introduces a new approach for the design of planar six-bar mechanisms for the purpose of function generation. The structural error is formulated using the input-output relationship of such a mechanism. In addition to the conventional structural error, its derivative is minimised via numerical optimisation, leading to the novel concept of dual-order structural error, which lends itself naturally to a multi-objective formulation of the design problem. Furthermore, analytical conditions for the mobility of the mechanism are derived for two cases: mobility for the full cycle of the crank, and for any given subset of it, along with the identification of the kinematic branches. These conditions help confine the numerical search for the optimal designs to the feasible regions of the design space, leading to a very efficient computational scheme. The results obtained are better in accuracy as compared to the reported results in existing literature. The formulation and results are demonstrated in the context of the Watt-II and the Stephenson-III mechanisms.
Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.
This paper describes an attitude control method to prevent the overturning of lunar and planetary landers. The proposed control method that is based on a variable-damping shock absorber for the landing gear is experimentally validated. Conventionally, the landing gear of lunar and planetary landers has a fixed shock attenuation parameter that is not used proactively for attitude control of the lander during the touchdown sequence. The proposed method suppresses any disturbance to the attitude of the lander by adjusting the damping coefficient of each landing leg independently, based on the angular velocity and displacement velocity of each landing leg. First, the control method for the variable damper is presented. Second, the result of a landing experiment conducted in a two-dimensional plane is shown. These results indicate that the proposed semi-active landing gear system is effective for preventing the overturning of the lander on inclined terrain.
This paper describes an attitude control method that has been designed to prevent the overturning of lunar and planetary landers, based on a variable-damping shock absorber for the landing gear. Conventionally, the landing gear of lunar and planetary landers has a fixed shock attenuation parameter that is not used proactively for attitude control of the lander during the touchdown sequence. The new method enables the suppression of any disturbance to the attitudeof the landerby adjusting the damping coefficient ofeach landing leg independently, based on the angular velocity vector and displacement velocity of each leg of the lander. The results of a numerical simulation indicate that the control rule for a three-dimensional system is effective for preventing the overturning of the lander on inclined terrain. The results of the simulation and experiments show that the landing gear with the actively variable damping and the control rule play a major role in preventing the overturning of a lunar or planetary lander. Copyright © 2016 by the American Institute of Aeronautics and Astronautics,.
This paper presents a design methodology for Stephenson II six-bar function generators that coordinate 11 input and output angles. A complex number formulation of the loop equations yields 70 quadratic equations in 70 unknowns, which is reduced to a system of ten eighth degree polynomial equations of total degree 810 = 1:07 × 109. These equations have a monomial structure which yields a multihomogeneous degree of 264,241,152. A sequence of polynomial homotopies was used to solve these equations and obtain 1,521,037 nonsingular solutions. Contained in these solutions are linkage design candidates which are evaluated to identify cognates, and then analyzed to determine their input-output angles in each assembly. The result is a set of feasible linkage designs that reach the required accuracy points in a single assembly. As an example, three Stephenson II function generators are designed, which provide the input-output functions for the hip, knee, and ankle of a humanoid walking gait.
The static-stability conditions for a many-legged walking apparatus with supporting points at the interior surface of a smooth horizontal cylinder and on two smooth planes are studied. For the cylinder, consequences of equilibrium conditions are considered under the assumption that reactions at the supporting points are directed along the radius of the cylinder. Under the additional assumption that the cylinder is a bilateral constraint, criteria for the solution of static equations for an apparatus that has no more than three supporting points are proposed. For the case where the cylinder is a unilateral constraint and there are no more than three supporting points, a classification of equilibrium positions (both isolated and those that form a connected set) is presented. Geometric criteria of a static stability are obtained for an arbitrary location of supporting points (if their number is no more than two) and for the case where there are three supporting points located at the surface of the lower semicylinder. For two parallel planes, the geometric criterion of the static stability is obtained, and for two intersecting planes a necessary condition for a solution of the problem of reaction distribution is obtained.
In this study, the general form of objective function and design constraints for the volume/weight of a gearbox has been written. The objective function and constraints can be used for any number of stages for gearbox ratio but in this paper one, two and three-stage gear trains have been considered and by using a Matlab program, the volume/weight of the gearbox is minimized. Finally, by choosing different values for the input power, gear ratio and hardness of gears the practical graphs from the results of the optimization are presented. From the graphs, all the necessary parameters of the gearbox such as number of stages, modules, face width of gears, and shaft diameter can be derived. The results are compared with those reported in the previous works and an example is presented to show how the practical graphs can be used.
Industry/NASA reusable launch vehicle (RLV) technology program efforts are underway to design, test, and develop technologies and concepts for viable commercial launch systems that also satisfy national needs at acceptable recurring costs. Significant progress has been made in understanding the technical challenges of fully reusable launch systems and the accompanying management and operational approaches for achieving a low-cost program.This paper reviews the current status of the RLV technology program including the DC-XA, X-33 and X-34 flight systems and associated technology programs. It addresses the specific technologies being tested that address the technical and operability challenges of reusable launch systems including reusable cryogenic propellant tanks, composite structures, thermal protection systems, improved propulsion, and subsystem operability enhancements. The recently concluded DC-XA test program demonstrated some of these technologies in ground and flight tests. Contracts were awarded recently for both the X-33 and X-34 flight demonstrator systems. The Orbital Sciences Corporation X-34 flight test vehicle will demonstrate an air-launched reusable vehicle capable of flight to speeds of Mach 8. The Lockheed-Martin X-33 flight test vehicle will expand the test envelope for critical technologies to flight speeds of Mach 15. A propulsion program to test the X-33 linear aerospike rocket engine using a NASA SR-71 high speed aircraft as a test bed is also discussed. The paper also describes the management and operational approaches that address the challenge of new cost-effective, reusable launch vehicle systems.
In the Apollo Program, the lunar-orbit rendezvous mode was used for the lunar-landing mission. To accomplish the lunar landing, a lunar module spacecraft was built. A description of the design requirements for the structural subsystem and of the structural configuration and the method of design verification are given. A discussion is presented of several problems encountered and the corrective actions taken during the designing, manufacturing, and testing of the lunar module.
Consider a legged robot at fixed foot placements. Where can the robot move its center of mass (CM) while remaining in static equilibrium? If the terrain is flat, the CM must lie above the convex hull of the robot's feet. If the terrain is not flat, this often-used approximation can be arbitrarily bad. Instead, the CM must lie above the projection of a nonlinear convex set that is defined by the properties of each foot placement. This paper presents an algorithm to compute the shape of this projection and gives a tight bound on the algorithm's running time. It also presents a method of amortizing the cost of this computation when it is only necessary to test static equilibrium at particular CM positions--that is, when it is only necessary to test the membership of points in the projection of a convex set rather than find its shape.
In this paper, we propose a successive gait-transition method for a quadruped robot to realize omnidirectional static walking. The gait transition is successively performed among the crawl gaits and the rotation gaits, while the feet hold in common positions before and after gait transition. The gait-transition time is reduced by carefully designing the foot positions of the crawl gait and the rotation gait, while limiting the feet in rectangular reachable motion ranges. Computer simulations and experiments were executed to show the validity and the limitation of the proposed gait-transition method.
Multi-objective evolutionary algorithms (MOEAs) that use
non-dominated sorting and sharing have been criticized mainly for: (1)
their O(MN3) computational complexity (where M is the number
of objectives and N is the population size); (2) their non-elitism
approach; and (3) the need to specify a sharing parameter. In this
paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II
(Non-dominated Sorting Genetic Algorithm II), which alleviates all of
the above three difficulties. Specifically, a fast non-dominated sorting
approach with O(MN2) computational complexity is presented.
Also, a selection operator is presented that creates a mating pool by
combining the parent and offspring populations and selecting the best N
solutions (with respect to fitness and spread). Simulation results on
difficult test problems show that NSGA-II is able, for most problems, to
find a much better spread of solutions and better convergence near the
true Pareto-optimal front compared to the Pareto-archived evolution
strategy and the strength-Pareto evolutionary algorithm - two other
elitist MOEAs that pay special attention to creating a diverse
Pareto-optimal front. Moreover, we modify the definition of dominance in
order to solve constrained multi-objective problems efficiently.
Simulation results of the constrained NSGA-II on a number of test
problems, including a five-objective, seven-constraint nonlinear
problem, are compared with another constrained multi-objective
optimizer, and the much better performance of NSGA-II is observed
Much lower launch costs make resupply cheaper than recycling for space life support
- H W Jones
The recent large reduction in space launch cost
- H W Jones