1. |
Nishanth Pushparaj, Yuta Hayashi, Mai Bando, Stabilization of Spacecraft in Spatial Periodic Orbits using Linear Quadratic Regulator (LQR), The 34th International Symposium on Space Technology and Science, 2023.06. |

2. |
Saki Takeuchi, Mai Bando, Shinji Hokamoto, Optimization of Structural Configurations of Spacecraft for Efficient Attitude Change Utilizing Non-holonomic Features, The 34th International Symposium on Space Technology and Science, 2023.06. |

3. |
Ayano Tsuruta, Mai Bando, Daniel J. Scheeres, Shinji Hokamoto, New Equilibria in Quadratic Optimal Control Systems, The 34th International Symposium on Space Technology and Science, 2023.06. |

4. |
Shodai Hirayama, Naoki Hiraiwa, Mai Bando, Shinji Hokamoto, Trajectory Design by Stochastic Gradient Descent Algorithm Adam, The 34th International Symposium on Space Technology and Science, 2023.06. |

5. |
Yuta Hayashi, Mai Bando, Shinji Hokamoto, Discrete-Time Attitude Control for Spacecraft Using Iterative Learning, The 34th International Symposium on Space Technology and Science, 2023.06. |

6. |
Zhengxu Pan, Mai Bando, Zhanxia Zhu and Shinji Hokamoto, A New Gravitational Wave Observatory Formation Configuration Design and Control Method, The 34th International Symposium on Space Technology and Science, 2023.06. |

7. |
Mai Bando, New Trends in Celestial Mechanics and Dynamical Astronomy, International Workshop on Celestial Mechanics and Dynamical Astronomy (IWCMDA-2023), 2023.01. |

8. |
Xi Chen, Mai Bando, Shinji Hokamoto, An Improved YOLO for Tiny Rocks Detection in Spacecraft Autonomous Landing Xi Chen, Mai Bando, Shinji Hokamoto, 2022 Asia-Pacific International Symposium on Aerospace Technology (APISAT2022), 2022.10. |

9. |
Naoki Hiraiwa, Mai Bando, Shinji Hokamoto, Design of Optimal Low-Thrust Orbit-to-Orbit Transfers via Convex Approach, 73rd International Astronautical Congress,, 2022.09. |

10. |
Kyosuke Sato, Mai Bando, Shinji Hokamoto, A Data-Driven Nonlinear Optimal Control Using Koopman Operator on Hamiltonian Flow, 73rd International Astronautical Congress,, 2022.09. |

11. |
Kanta Ikeda, Naoki Hiraiwa, Mai Bando, Shinji Hokamoto, Design of Satellites Tours Using Periapsis Poincar\'{e} Map in Multibody Dynamics of Jovian System, 73rd International Astronautical Congress,, 2022.09. |

12. |
Taiga Kajikawa, Mai Bando, Shinji Hokamoto, Data-Driven Guidance for Asteroid Landing Based on Real-Time Dynamic Mode Decomposition, 73rd International Astronautical Congress,, 2022.09. |

13. |
Hiromitsu Hiraiwa, Mai Bando, Shinji Hokamoto,, Altitude Estimation by Wide-Field-Integration Optic Flow, 33rd Congress of the International Council of the Aeronautical Sciences, 2022.09. |

14. |
Yuke Huang, Mai Bando, Shinji Hokamoto, Influence of Overall Layout Design of Compound Multi-Rotor Vehicles on Flight Performance, 33rd Congress of the International Council of the Aeronautical Sciences, 2022.09. |

15. |
Komsun Tamanakijprasart，Mai Bando，Shinji Hokamoto, Data-Driven Orbital Control in Perturbed Environment, SICE Annual Conference 2022, 2023.09. |

16. |
Erica L. Jenson，Mai Bando，Kyosuke Sato, Daniel J. Scheeres, Robust Nonlinear Optimal Control Using Koopman Operator Theory, 2022 AAS/AIAA Astrodynamics Specialist Conference, 2022.08. |

17. |
Saki Takeuchi, Kanta Ikeda, Mai Bando, Shinji Hokamoto, Effects of Rotational Joint Directions of Variable Structure on Non-holonomic Features, The 33rd International Symposium on Space Technology and Science, 2022.02. |

18. |
Naoki Hiraiwa, Mai Bando, Shinji Hokamoto, Halo-to-Halo Low-Thrust Transfer via Successive Convex Optimization with Intermediate Orbit Design, The 33rd International Symposium on Space Technology and Science, 2022.02. |

19. |
Kanta Ikeda, Naoki Hiraiwa, Mai Bando, Shinji Hokamoto, Design of low energy transfer trajectories from Earth to Europa with ballistic capture, The 33rd International Symposium on Space Technology and Science, 2022.02. |

20. |
Yuto Hirose, Mai Bando, Shinji Hokamoto, Spacecraft Trajectory Design Using Data-Driven Model Predictive Control, 72nd International Astronautical Congress, 2021.10. |

21. |
Naoki Hiraiwa, Mai Bando, Shinji Hokamoto, Analysis of Ballistic Escape Based on Lobe Dynamics, 72nd International Astronautical Congress, 2021.10. |

22. |
Yoshiki Matsumura, Mai Bando, Shinji Hokamoto, Multirotor Vehicles Design Based on Dynamic Manipulability for Underactuated Flying Systems, 32nd Congress of the International Council of the Aeronautical Sciences, 2021.09. |

23. |
Kyosuke Sato, Mai Bando and Shinji Hokamoto, A Data-Driven Nonlinear Optimal Control of Unstable Fixed Points, 2021 AAS/AIAA Astrodynamics Specialist Conference, 2021.08. |

24. |
Taiki Urashi, Mai Bando and Shinji Hokamoto, Data-Driven Analysis of Chaotic Orbits in the Circular Restricted Three Body Problem, 2021 AAS/AIAA Astrodynamics Specialist Conference, 2021.08. |

25. |
Yuki Oshima, Mai Bando, Shinji Hokamoto, Trajectory design in the circular restricted three-body problem using artificial invariant manifolds, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, 2019.01, This paper generalizes the invariant manifolds of unstable libration point orbits through the application of continuous thrust. Considering Jacobi constant of the end of invariant manifolds, an artificial periodic orbit around a libration point realizes heteroclinic connections between itself and an unforced periodic orbit with same Jacobi constant of the end of invariant manifolds. Heteroclinic connections between libration point orbits are constructed by detecting intersections of states of manifolds on the Poincaré map. We reveal low-energy spacecraft can transfer to some periodic orbits with different Jacobi constant. In addition, this paper defines New Jacobi constant of low-thrust spacecraft. By utilizing new Jacobi constant, we illustrate zero-velocity curves of low-thrust spacecraft and reveal that there is a crack of zero-velocity curves and spacecraft can pass the crack.. |

26. |
Yuki Kayama, Mai Bando, Shinji Hokamoto, Sparse optimal trajectory design in three-body problem, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, 2019.01, A structure of the optimal trajectory for minimizing fuel consumption in an unstable dynamical environment such as the three-body problem is not well studied. Recently, it has been found that a sparse solution structure appears in the optimal control of a dynamical system. The concept of sparsity explains the property that the minimum fuel trajectory corresponds to the trajectory which minimizes the total thrusting time. In this paper, we propose a numerical method to obtain the minimum fuel sparse optimal trajectory in the unstable dynamical system. As an example, proposed methods are applied to the transfer in the Sun-Earth system.. |

27. |
Mohamed Shouman, Mai Bando, Shinji Hokamoto, Output regulation control for satellite formation flying using differential drag, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, 2019.01, This paper proposes a new hybrid control action of differentials aerodynamic drag and thrusters to control satellite formation flying in low Earth orbits. Parameterized output regulation algorithm for formation flying missions is developed based on the Schweighart-Sedwick relative dynamics equations. It is implemented to precisely track the different trajectories of reference relative motion and eliminates the effects of the J_{2} perturbations. Parametric Lyapunov algebraic equation is derived to ensure the stability of the linear relative model subject to saturated inputs. The main goal of this study is to approve the viability of using the differentials in aerodynamic drag to precisely control different formation flying missions. Numerical simulations using a high fidelity relative dynamics model are implemented to analyze the performance of the proposed control algorithm in comparison with the linear quadratic regulator algorithm for actual satellite parameters. The paper exploits a high-precision orbit propagator model to verify the robustness of the control algorithm.. |

28. |
Mohamed Shouman, Mai Bando, Shinji Hokamoto, Controllability analysis of propellant-free satellite formation flight, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, 2019.01, This paper proposes the controllability analysis of relative motion using different configurations for hybrid control actions of space environmental forces. It tends to present a minimal configuration for the missions exploiting these forces. It illustrates the constraints in each space environmental force and analyzes the integration between these forces to achieve full controllability of the satellite formation flight for near-circular low earth orbits with different orbit configurations. The paper implements a Kalman decomposition approach to decompose the system into controllable and uncontrollable subspaces for linear time-invariant control actions. Numerical simulations are investigated to study the controllability analysis for nonlinear models and substantiate the success of the controllability study for all hybrid control actions with different orbit configurations.. |

29. |
Kyosuke Asaki, Mai Bando, Shinji Hokamoto, Riemannian optimization for spacecraft trajectory design, 70th International Astronautical Congress, IAC 2019, 2019.10, Many of the equations of motion appearing in the aerospace field are nonlinear, and the problem of input optimization under this equation of motion is important. There are two methods for solving the nonlinear optimal control problem: direct method and indirect method. In the direct method, the equation of motion is discretized, and the problem is solved as a nonlinear programming problem with motion equations as constraints. In the direct method, it is possible to solve the problem by adding various constraints, but the solution becomes complicated and it is difficult to guarantee the convergence to the optimal solution. In this study, we consider a set of unknowns that satisfy constraints as Riemannian manifolds, and treat the problem as an unconstrained optimization problem on Riemannian manifolds. A simplified rocket trajectory optimization problem illustrates the proposed method.. |

30. |
Yuri Hachiya, Yuki Kayama, Mai Bando, Shinji Hokamoto, Manifold-to-manifold transfers using low-thrust acceleration, 70th International Astronautical Congress, IAC 2019, 2019.10, This paper considers manifold-to-manifold transfers in the circular-restricted three-body problem enabled by low-thrust acceleration where an initial and target states lie on invariant manifolds associated to libration point orbits with different Jacobi constant. The basic idea is to utilize a family of stable and center manifolds that lie arbitrarily close to the target invariant manifold to reduce the cost of transfer. The linear quadratic regulator is used to design feedback control to transfer to the target manifold. Time invariant and time periodic controlleres are derived based on the linearized motion around the equilibrium point and periodic orbit respectively. The results show that the feedback controller can shape the linearized motion around manifold to be that around the equilibrium point or a periodic orbit. As a demonstration, transfer trajectories are designed to target the unstable manifold associated with an unstable Lyapunov orbit in the Earth-Moon system.. |

31. |
Y. Zhou, M. Bando, S. Hokamoto, P. L. Wu, Manifold-based robust stationkeeping of libration-point orbit with navigational uncertainty, 70th International Astronautical Congress, IAC 2019, 2019.10, This paper investigated the manifold-based robust stationkeeping approach for the halo orbit near the Earth-Moon L2 point in the ephemeris model. The well-known Hamiltonian structure-preserved (HSP) method is utilized to design the controller for stationkeeping. However, conventional HSP method is proposed under the ideal condition, where the equations of motion are constructed in the circular restricted three-body problem, and the navigational uncertainty is not considered as well. Actually, these uncertainties always exist and have significant influence on the performance of stationkeeping. To make the results more realistic, the dynamics in the ephemeris model is used to describe the motion of a spacecraft. A filtering structure-based navigation is incorporated in the stationkeeping, where the navigational uncertainty is introduced. In addition, the navigation filter is reformed to compensate for the control uncertainty. Simulation is performed to observe the influence of the control gain and the magnitude of the uncertainty on the stationkeeping performance.. |

32. |
Satoshi Nagashima, Mai Bando, Shinji Hokamoto, Optimal trajectory design for safety rendezvous based on sparse modeling, 69th International Astronautical Congress: #InvolvingEveryone, IAC 2018, 2018.10, In trajectory design of a spacecraft, reducing the fuel consumption is important factor. In order to find the minimum fuel trajectory, this paper considers the L ^{1} norm as the performance index. This paper discuss design parameters characterizing the L ^{1} optimal trajectory, such as sampling time, flight time and magnitude of thrust. Also, this paper compare with the conventional method from the viewpoint of fuel consumption. In addition, this paper consider the rendezvous problem considering safety.. |

33. |
Tomoya Sakamoto, Mai Bando, Shinji Hokamoto, Optimal control of spacecraft attitude motion using Port-Hamiltonian systems, 69th International Astronautical Congress: #InvolvingEveryone, IAC 2018, 2018.10, In this study, a concept of optimality is introduced into Port-Hamilton systems for attitude control of spacecraft. Port-Hamiltonian systems make it possible to design asymptotically stable controllers in a uniform procedure for a wide variety of physical systems. By introducing optimality to Port-Hamilton system, conventional error systems of Port-Hamilton systems are expanded to minimize a quadratic form of evaluation function. In this study, as an optimal control method of Port-Hamiltonian system, Hamilton-Jacobi-Bellman (HJB) equation is considered. Since solving HJB equation is not easy, the equation is simplified through generalized canonical transformation, which is a unique conversion of Port-Hamiltonian system. Furthermore, by considering the minimum evaluation function as a Hamiltonian transformed through the generalized canonical transformation, the analytical solution of the HJB equation can be derived. This method can be used for a time-varying error system and applied for tracking control of spacecraft to specified trajectories. The optimality of the control input obtained from the proposed procedure is verified in numerical simulations.. |

34. |
Yang Zhou, Mai Bando, Shinji Hokamoto, Panlong Wu, Influence of unstable dynamics on orbit determination with x-ray pulsar navigation, 4th IAA Conference on Dynamics and Control of Space Systems, DYCOSS 2018, 2018.05, This paper explores the influence of unstable dynamics on orbit determination. A halo orbit about the Earth-Moon L2 is considered to be the nominal orbit and the dynamics model is constructed based on the Earth-Moon circular restricted three body problem. X-ray pulsar navigation method is introduced for orbit determination that is performed by Kalman filter. Simulation results show that unstable manifold of halo orbit dominates the growth of orbit-determination error and the corresponding uncertainty. However, when the orbit-determination measurements are incorporated in, the results change and are greatly influenced by the characteristic of the X-ray pulse measurements.. |

35. |
Yuki Akiyama, Mai Bando, Shinji Hokamoto, Extended state space approach for trajectory design in elliptic restricted three-body problem, 69th International Astronautical Congress: #InvolvingEveryone, IAC 2018, 2018.10, This paper presents novel methods to provide libration point orbits (LPOs) and invariant manifolds (IMs) associated with libration point orbits in the elliptic restricted three-body problem (ERTBP). First, we introduce an extended autonomous system to describe the ERTBP. By introducing an autonomous system which generates a periodic function and integrating it with the ERTBP which is non-autonomous, we can obtain the extended autonomous system. Then, the center manifold design method which can uniquely provide an LPO in the circular restricted three-body problem is applied to the ERTBP. Next, we present a design method for IMs in the ERTBP by using the local stability characteristics obtained by the state transition matrix along LPOs of the extended system. The proposed design methods are applied and verified for the Earth-Moon L _{1} ERTBP. We show various LPOs in the ERTBP by changing design parameters, and IMs associated with a libration point and an LPO.. |

36. |
Nobuki Yamaguchi, Mai Bando, Shinji Hokamoto, Trajectory design to triangular libration points based on resonant orbits, 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017, 2017.09, In this paper, we extend the flow function method for finding resonant orbits. The relation between flow function, resonance number and order of the resonant orbit are revealed. The resonant orbits design in the Sun-Earth CRTBP are demonstrated and the results show that the resonant orbits can be found globally and systematically by the flow function method. The flow function method can also be applied to obtain higher order resonant orbits. As an application, we propose a transfer trajectory to the L_{4}/L_{5} SPOs by using various resonant orbits. Our results reveals that two types of insertion is possible for SPO insertion with small ΔV.. |

37. |
Motoki Yamane, Mai Bando, Shinji Hokamoto, Formation flying along elliptical orbit using attractive sets of optimal control, 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017, 2017.09, This paper proposes a new method of optimal trajectory design for formation flying along an elliptical orbit. Under linearized assumptions and a quadratic performance index, the optimal cost is quadratic in the initial state. Attractive sets of optimal control are defined as contours of the optimal cost based on linear quadratic regulator theory. It describes a set of all initial states to reach a desired state by a given cost. By solving the optimal control problem for TH equations, the optimal cost is obtained as a time-periodic function. This paper develops the attractive set for a time-periodic system and procedure to draw the attractive set is shown. The advantage of using attractive sets for optimal trajectory design is that it can determine the optimal initial state immediately. The various shape of the periodic orbit and the attractive sets are demonstrated by weight parameters of optimal control theory.. |

38. |
Yuki Akiyama, Mai Bando, Shinji Hokamoto, Quaternion based attitude stabilization in the circular restricted three-body problem, 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017, 2017.09, This paper presents a novel method to realize station-keeping and control attitude motion simultaneously on a libration point orbit based on the nonlinear output regulation. First, the coupled orbit-attitude motion of a rigid spacecraft subject to three-body dynamics is formulated using the quaternion. Next, the reference orbit and attitude are represented as the output of an autonomous system called exosystem, assuming the reference orbit and attitude are given by a truncated Fourier series. Then the controller is derived by solving the output regulation problem. The derived controller has the explicit form and can achieve the asymptotically tracking for any reference orbit and attitude represented in the Fourier series. The proposed controllers are applied and verified for the Sun-pointing attitude control and station-keeping along Sun-Earth L_{2} Halo orbits.. |

39. |
Naoto Kobayashi, Mai Bando, Shinji Hokamoto, Optic flow-based navigation system for planetary rovers, 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017, 2017.09, This paper proposes a novel optic flow-based navigation system for planetary rovers. Optic flow is a vector field of relative velocities between the camera mounted on a rover and environments, and it is often utilized for motion estimations or relative distance estimations. However, only either one of them can be estimated in general optic flow processing. The method proposed in this paper enables both of the estimations by utilizing an image segmentation technique in computer vision and applying Wide-Field-Integration (WFI) of optic flow for robust estimations. Thus, both obstacle avoidance and avoidance of getting stuck, which are key technologies for planetary exploration rovers, are realized in the method. Furthermore, since the estimation is accomplished in linear processing, a real-time estimation is possible by onboard computers. The effectiveness of the proposed method is examined through numerical simulations, considering sensor noises and the shape of obstacles.. |

40. |
Yuki Akiyama,Mai Bando,Shinji Hokamoto,, Station-keeping and formation flying based on Nonlinear Output Regulation Theory, 9th International Workshop on Satellite Constellations and Formation Flying (IWSCFF), 2017.06. |

41. |
Motoki Yamane,Mai Bando,Shinji Hokamoto,, Optimal Trajectory Design of Formation Flying based on Attractive sets, 31st International Symposium on Space Technology and Science (ISTS),, 2017.06. |

42. |
Tomohito Sekiguchi,Saki Omi,Mai Bando,Shinji Hokamoto,, Dynamic Locomotion of a Multi-Legged Planetary Exploration Rover with Isotropic Leg Arrangement, 31st International Symposium on Space Technology and Science (ISTS),, 2017.06. |

43. |
Tomoya Sakamoto, Yuki Akiyama, Mai Bando, Shinji Hokamoto, Considerations on design parameters for attitude control of spacecraft using port-controlled Hamiltonian systems, 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017, 2017.11, In previous research, a controller design procedure via generalized canonical transformations has been proposed to keep the passivity feature of Port-controlled Hamiltonian systems. The procedure has a general form and is applicable to spacecraft's attitude motion described with quaternion parameters. This paper investigates the roles of several design parameters in the generalized canonical transformations. Special attention is placed on the relation between the shape of Lyapunov functions and the convergence speed of the state variables. Furthermore, from the analysis utilizing the linearized form of the Port-controlled Hamiltonian system, the guideline to decide the preferable ratio between two parameters in the design procedure is proposed.. |

44. |
Mai Bando, Daniel J. Scheeres, Nonlinear attractive sets under optimal feedback control in the hill three-body problem, AIAA/AAS Astrodynamics Specialist Conference, 2016, 2016.09, Trajectory design combining low-thrust and the three-body problem is a challenging area for study. This paper investigates the combination of optimal feedback control with the dynamical structure of the three-body problem. For the nonlinear system, the attractive set of an equilibrium point or a periodic orbit under optimal control is described by the Hamilton-Jacobi-Bellman partial differential equation. We obtain the solution to the Hamilton-Jacobi-Bellman equation by solving the truncation problem successively.. |

45. |
Mai Bando, Daniel J. Scheeres, Attractive set of optimal feedback control for the hill three-body problem, 26th AAS/AIAA Space Flight Mechanics Meeting, 2016, 2016.02, This paper investigates the combination of optimal feedback control with the dynamical structure of the three-body problem. The results provide new insights for the design of continuous low-thrust spacecraft trajectories. Specifically, we solve for the attracting set of an equilibrium point under optimal control with quadratic cost. The analysis reveals the relation between the attractive set and original dynamics. In particular, we find that the asymptotic form of the attractive set to an equilibrium point or a fixed point under optimal control is completely defined by its left unstable eigenvectors and a term inversely proportional to its unstable eigenvalue.. |

46. |
Tsubasa Yamasaki, Mai Bando, Shinji Hokamoto, Powered swing-by using tether cutting, 67th International Astronautical Congress, IAC 2016, 2016.09, The swing-by maneuver is known as a method to change the velocity of a spacecraft by using the gravity force of the celestial body. The powered swing-by has been proposed and researched to enhance the velocity change during the swing-by maneuver, e.g. Prado (1996). The research reports that applying an impulse maneuver at periapsis maximizes the additional effect to the swing-by. However, such impulsive force requires additional propellant. On the other hand, Williams et al. (2003) researched to use a tether cutting maneuver for a planetary capture technique. This current paper studies another way of the powered swing-by using tether cutting, which does not require additional propellant consumption. A Tethered-satellite is composed of a mother satellite, a subsatellite and a tether connecting two satellites. In a swing-by trajectory, a gravity gradient force varies according to the position of the tethered-satellite, and consequently its attitude motion is induced; the tethered-satellite starts to liberate and rotate. Cutting the tether during the tethered-satellites' rotation can add the rotational energy into the orbital energy. In this research, since the gravity gradient effect on orbital motion is small, the orbit can be considered a hyperbolic orbit. Assuming that the tether length is constant, Eq. (1) describes the equation of the attitude motion of a tethered-satellite within the SOI (sphere of influence) of the secondary body. θ = 1/1+ e cos α {2e (θ' + 1) sin α - 3/2 sin 2θ} where e is an orbit eccentricity, α is a true anomaly, θ is an attitude angle and l is tether length. The prime means the derivative with α. The mother satellite and subsatellite can obtain not only the velocity change but the position change by the tether cutting; they are denoted as Δv and Δr, and described in Eqs. (2) and (3), respectively. Δv = -l_{1}(α + θ) [-sin (α + θ) cos (α + θ)] Δr = -l_{1} [cos (α + θ) sin (α + θ)] where l_{1} is a distance between the center of gravity of the tethered-satellite and the mother satellite. Since α and θ are functions of time, Δv and Δr are also functions of time. This means that changing the tether cutting point can maximize the velocity change in this proposed powered swing-by maneuver. Furthermore, the optimum cutting point depends on the attitude and angular velocity when the tethered satellite enters the SOI. We propose a systematic design procedure to obtain the desired velocity change by optimizing the cutting point, the initial attitude and the initial angular velocity of the tethered satellites.. |

47. |
Yuki Akiyama, Mai Bando, Shinji Hokamoto, Periodic orbits design based on the center manifold theory in the circular restricted three-body problem, 67th International Astronautical Congress, IAC 2016, 2016.09, Invariant manifolds such as stable and unstable manifolds are often used in trajectory designs in the circular restricted three-body problem (CRTBP). Focusing on center manifolds, this paper proposes a simple but powerful trajectory design method for a periodic orbit based on the center manifold theorem. In general, there exist three types of invariant manifolds around equilibrium points: stable, unstable and center manifolds. The trajectories on center manifolds are bounded, whereas those on stable or unstable manifolds exponentially approach or diverge from the libration point as time passes. Hence, periodic orbits can be considered as systems lying on center manifolds. A general system around an equilibrium point is given by (Equation presented) where f, g and h are nonlinear terms and all real-parts of eigenvalues of matrices C, P and Q are zero, negative and positive, respectively. According to the center manifold theorem, in the neighborhood of the equilibrium point, the system (1) can be represented by (Equation presented) The first ordinary differential equation is called reduced order system. The solution to Eq. (2) represents solutions restricted on center manifolds. Based on Eq. (2), we propose a novel method to obtain periodic orbit. It includes two steps. The first step computes approximate solutions for the system shown as Eq. (2) in the CRTBP. This step requires iteration by using a successive approximation method proposed by Suzuki et al., which requires initial values of the reduced order system, ξ ∈ R ^{4} . Note that since in the first step quasi-periodic orbits are obtained, a further modification of ξ is necessary to obtain pure periodic orbits. The second step corrects ξ to form a periodic orbit. The required variation Δξ are computed by using the state transition matrix. The remarkable feature of the proposed method is that once we fix three components of ξ, the method provides the initial state for a periodic orbit uniquely by successive iteration mentioned above. Note that two of them become zero from symmetries of periodic orbits and the rest can be set arbitrarily. Contrary to the proposed method, conventional methods such as the differential correction method and the Lindstedt-Poincaré method require good initial guesses and complex algebraic manipulations. The proposed method is applicable to any equilibrium point, although as an example the proposed method is applied to the Sun-Earth L _{2} point and verified in numerical simulation. In conclusion, we reveal that the proposed method is a very powerful tool and can significantly reduce efforts to obtain periodic orbits.. |

48. |
Mai Bando, Hamidreza Nemati, Shinji Hokamoto, Satellite formation-keeping about libration points in the presence of system uncertainties, AAS/AIAA Astrodynamics Specialist Conference, ASC 2015, 2016, This paper studies a control law to stabilize the orbital motion in the vicinity of an unstable equilibrium points and periodic orbits in the circular-restricted three-body problem. Utilizing the eigenstructure of the system, the fuel efficient formation flying controller via linear quadratic regulator (LQR) is developed. Then the chattering attenuation sliding mode controller (CASMC) is designed and analyzed for the in-plane motion of the circular circular-restricted three-body problem. Simulation studies are conducted for the Sun-Earth L_{2} point and a halo orbit around it. The total velocity change required to reach the halo orbit as well as to maintain the halo orbit is calculated. Simulation results show that the chattering attenuation sliding mode controller has good performance and robustness in the presence of unmodeled nonlinearity along the halo orbit with relatively small fuel consumption.. |

49. |
Hamidreza Nemati, Mai Bando, Shinji Hokamoto, Design of sliding mode controllers for formation flying along unstable periodic orbits in CR3BP, 66th International Astronautical Congress 2015: Space - The Gateway for Mankind's Future, IAC 2015, 2015, This paper studies a control law to stabilize the orbital motion in the vicinity of an unstable equilibrium point and periodic orbits in the circular-restricted three-body problem (CR3BP). Since the libration point orbits especially around collinear points are highly unstable, time-delay in sensor and/or acutor might cause instability. In this paper, we derive a continuous sliding mode controller (Cont. SMC) to achieve robust fuel-efficient periodic motion based upon a new Lyapunov function to smooth the control input. Then, the total velocity change is investigated to reach and maintain a halo orbit in the Sun-Earth CR3BP. Simulation results show that the proposed Cont. SMC has good performance and robustness in the presence of unmodeled time-delay.. |

50. |
Mai Bando, Akira Ichikawa, Optimal selection of impulse times for formation flying, 2nd International Academy of Astronautics Conference on Dynamics and Control of Space Systems, DyCoSS 2014, 2015, In this paper, leader-follower formation flying problems based on the periodic orbits of the Hill-Clohessy-Wiltshire equations and Tschauner-Hempel equations are considered. the control input is assumed to be impulsive. For a given final relative orbit, the admissible controls are feedback controls such that the follower tracks the final orbit asymptotically. The main performance index is the ΔV which is proportional to the fuel consumption. The number of impulses is fixed, but the impulse time is arbitrary and varied. The optimal location of impulse times is sought numerically. Simulation results for a reconfiguration problem are given.. |

51. |
Mai Bando, Naoki Date, Shinji Hokamoto, Estimation of mean orbital elements with unknown low-thrust acceleration, 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014, 2014, Space Situational Awareness (SSA) has been recognized to be important for the safe space activities including these problems. As low-thrust propulsion technology becomes increasingly popular, SSA for low-thrust spacecraft may become an area of increasing interest. More frequently use of low-thrust propulsion to place satellites in orbit create more opportunities for collisions and radio frequency interference as these spacecraft travel slowly through altitude ranges. The purpose of this paper is to develop a method for estimation of the mean orbital elements for low-thrust spacecraft. To overcome the instability of the estimation problem with low-thrust acceleration, we estimate the mean elements instead of osculating elements. By use of the averaging technique, Hudson and Scheeres (2009) proposed an analytical model of secular variations of orbital elements under thrust acceleration. The resulting averaged equation has a nice property in which only finite number of Fourier coefficients of the thrust acceleration appear because of the orthogonality of the trigonometric function. Based on the nonlinear state equation representation for the extended state variable which include not only orbital elements but also unknown Fourier coefficients, mean orbital elements and thrust history are estimated from observation data of mean orbital elements. Moreover, the mapping from mean to osculating elements is derived which can be replaced by a measurement equation. Proposed method is demonstrated through numerical simulations. |

52. |
Shinji Hokamoto, Masataka Oishi, Naoto Kobayashi, Mai Bando, Wide-field-integration of optic flow for realistic estimation system for space probes, 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014, 2014, This study discusses the condition of Wide-Field-Integration (WFI) of optic flow to make it as a realistic guidance and navigation system for space probes. WFI of optic flow is a bio-inspired navigation system mimicking visual processing system of flying insects using their compound eyes. However, in a real system, photoreceptors on a spherical surface used in WFI of optic flow are replaced by pixels on flat image surfaces of cameras, and the camera's field of view is limited. This paper examines the effect of the realistic restrictions for WFI of optic flows on the estimation performance in numerical simulations. The estimation accuracy is evaluated for several parameters: the field of view and the resolution of a camera, which is used instead of photoreceptors. Effects of space probe motion and sensor noises are also evaluated. It is shown that a camera with a wider field of view shows better accuracy, when the total number of pixels (or photoreceptors) is same.. |

53. |
Mai Bando, Akira Ichikawa, Formation flying along an elliptic orbit by pulse control, 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013, 2014, The linearized equations of relative motion of a follower satellite with respect to the leader in a given elliptic orbit are described by Tschauner-Hempel (TH) equations. In this paper, formation flying for the TH system with pulse control input is considered. First, the reconfiguration problem where the desired relative orbit of the follower is natural periodic orbit. Next, the active formation problem where the desired relative orbit is generated by an exosystem is considered. This allows for flexibility of the shape and period of the reference orbit. To realize such a formation flying, the output regulation theory for linear periodic systems is employed. To achieve asymptotic tracking, stabilizing feedback controls are designed by the periodic solution of discrete-time Riccati equation of the linear quadratic regulator (LQR) theory.. |

54. |
Mai Bando, Yuki Akiyama, Shinji Hokamoto, Robust deflection strategies of Near Earth asteroids under uncertainties, 24th AAS/AIAA Space Flight Mechanics Meeting, 2014, 2014, In this paper, an approach to optimize deflection mission of Near Earth asteroids under uncertainty is proposed based on control theoretical framework. By using the nonlinear mapping from initial deviation to the final deviation, the performance index J which is expressed as a function of the distance of the Earth in the Earth's closest approach time is minimized for the worst case initial condition. We also formulate the robust orbital transfer problem of kinetic impactor spacecraft where the initial state estimation error exists.. |

55. |
Mai Bando, Masaki Nakamiya, Yasuhiro Kawakatsu, Chikako Hirose, Takayuki Yamamoto, Trajectory design of destiny mission, 13th International Space Conference of Pacific-Basin Societies, ISCOPS 2012, 2013.04, The trajectory design of the interplanetary mission "Demonstration and Experiment of Space Technology for INterplanetary voYage, DESTINY" is discussed. The trajectory optimization of low-thrust spacecraft pose a difficult design challenge. Moreover, DESTINY mission requires many constraints for the orbital design. In advance of optimizing the whole transfer mission, we investigated the basic theory to design which can take into account such constraints.. |

56. |
Mai Bando, Akira Ichikawa, Active formation along a circular orbit by pulse control, 2013 52nd Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2013, 2013, The relative motion of a follower satellite with respect to the leader in a given circular orbit is described by autonomous nonlinear differential equations. The linearized equations around the null solution are known as Hill- Clohessy-Wiltshire (HCW) equations. In this paper, active formation flying for the HCW system with pulse (impulse) control input is considered, where the desired relative orbit of the follower is generated by an exosystem. This allows for flexibility of the shape and period of the reference orbit. The output regulation theory for discrete linear system is employed. To show the effectiveness of this approach, numerical examples are given.. |

57. |
K. Osuka, H. Mochiyama, K. Tadakuma, Mai Bando, K. Ohgata, Proposal of buckling-type-driving-unit for rover on small gravity asteroid, 2013 52nd Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2013, 2013, In this note, we propose a new driving unit for a rover on small gravity asteroid MINERVA-II. MINERVA-II will be carried by Hayabusa-2 which will be carried by H-IIA rocket launched in 2014. In designing the rover, the most difficult point is lack of information of the target asteroid. To overcome this diffilulty, we propose a kind of passive type driving system. Concretely, we try to apply buckling phenomenon and use spring. As the result, very simple driving unit for unknown field will be developed.. |

58. |
Mai Bando, Akira Ichikawa, Formation flying along a circular orbit with control constraints, 2011 AAS/AIAA Astrodynamics Specialist Conference, ASTRODYNAMICS 2011, 2012, In this paper, leader-follower formation flying problems based on the periodic orbits of the Hill-Clohessy-Wiltshire equations are considered. For a given final relative orbit, the admissible controls are feedback controls such that the follower tracks the final orbit asymptotically. The main performance index is the L_{1}-norm of the control input which is proportional to the fuel consumption. The L_{∞}-norm, which gives the magnitude of the input, is an additional performance index under the thruster level limitation. Feedback controls are designed via two algebraic Riccati equations with parameters, and their L_{1}- and L_{∞}- norms are given as functions of the parameters. Suboptimal controls are designed by choosing appropriate parameters. Simulation results for a reconfiguration problem are given to demonstrate the effectiveness of the design method.. |

59. |
Takao Fujii, Koichi Osuka, Mai Bando, On the optimality of plug-in optimal control systems, 2012 International MultiConference of Engineers and Computer Scientists, IMECS 2012, 2012, We consider a plug-in control system via a concept of Implicit and Explicit Controls as the two stage controllers. We first show two conditions under which the plug-in control system can be optimized by a suitable design of explicit control in the 2nd stage, when an implicit control is given in the 1st stage. We then show another condition under which the resultant optimal cost can be minimized by a suitable design of the Is' stage implicit control, which is characterized as a feedback control that allocates all the closed-loop poles onto the imaginary axis. These two results clarify the system theoretic meaning of the implicit control from the viewpoint of inverse optimal control problem.. |

60. |
Koichi Osuka, Takao Fujii, Mai Bando, On optimality and integrity of plug-in optimal control, 50th Annual Conference on Society of Instrument and Control Engineers, SICE 2011, 2011, In this note, we consider a plug-in control system via a concept of Implicit Control and Explicit Control. We show that the plug-in control system can be optimized by a certain plug-in control law. And also we show that a property of integrity can be embedded in the optimal plug-in control system.. |

61. |
Mai Bando, Koichi Osuka, Takao Fujii, Hiroshi Yamakawa, Orbital maintenance for observation mission of peanut-shaped asteroid, 50th Annual Conference on Society of Instrument and Control Engineers, SICE 2011, 2011, In this paper, we consider the motion control of spacecraft in the vicinity of the peanut-shaped asteroid. The implicit control concept is studied and orbital maintenance strategy to observe the peanut-shaped asteroid where the model of the gravity field is difficult to obtain is proposed. The implicit control law is characterized in terms of inverse problem of optimal control.. |

62. |
Hiroshi Yamakawa, Mai Bando, Katsuyuki Yano, Shu Tsujii, Spacecraft relative dynamics under the influence of geomagnetic lorentz force, AIAA/AAS Astrodynamics Specialist Conference 2010, 2010.12, The motion of a charged satellite subjected to the Earth's magnetic field is considered. Lorentz force, which acts on charged particle when it is moving through the magnetic field, provides a new concepts of propellant-less electromagnetic propulsion. We derive a dynamical model of a charged spacecraft including the effect of Lorentz force in the vicinity of circular and elliptic orbit and consider its application to formation flight. Based on Hill-Clohessy-Wiltshire equations and Tschauner-Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on linearized equations in the equatorial case show that the stability of the periodic solutions. Numerical simulations revealed that the periodic solutions which are useful for the formation are obtained for both circular and elliptic reference orbits.The control strategy for the propellantless rendezvous and reconfiguration are developed.. |

63. |
Mai Bando, Akira Ichikawa, Active formation along an eccentric orbit, 18th IFAC Symposium on Automatic Control in Aerospace, ACA 2010, 2010.01, In this paper, a formation problem of a spacecraft with a leader in an elliptic orbit is considered, where the follower is required to track asymptotically a given periodic relative orbit. The linearized equations of relative motion along an eccentric orbit are known as Tschauner-Hempel equations. The Tschauner-Hempel equations are transformed into simpler ones by the change of variables. For the transformed system, the active formation problem is formulated, and feedback controllers are designed by the regulator equations associated with the Hill-Clohessy-Wiltshire equations. Feedback controllers are also designed using a DRE associated with the TH equations, and the Li-norms of designed controllers are compared.. |

64. |
Hiroshi Yamakawa, Mai Bando, Gravity-coulomb force combined three-body problem, 18th IFAC Symposium on Automatic Control in Aerospace, ACA 2010, 2010.01, The aim of this paper is to investigate the dynamics of a restricted three-body problem governed by two types of forces: gravity force and Coulomb force. The electrostatic charging and hence the Coulomb force is introduced in order to change the relative position by positive control of the charge amount without using fuel expenditure.. |

65. |
Mai Bando, Hiroshi Yamakawa, Application of global solution of Hamilton-Jacobi equations to optimal low-thrust multiple rendezvous problem, 61st International Astronautical Congress 2010, IAC 2010, 2010, This paper presents a procedure to design multiple rendezvous missions. We propose a new low-thrust trajectory optimization method to find the optimal trajectory in analytical form. The resulting control law is a feedback control, so that it is effective in overcoming sensitivities to small variations in initial orbit and thrust profile. This study determines the optimal approach to find an effective control law to sequential transfer problem. For comparison, optimal sequence using impulsive and continuous thrust method are investigated. Our approaches are illustrated through the trajectory design of the multiple flyby mission and resulting fuel costs are compared.. |

66. |
Hiroshi Yamakawa, S. Hachiyama, Mai Bando, Atitude dynamics of a pendulum-shaped charged satellite, 61st International Astronautical Congress 2010, IAC 2010, 2010, Orbiting artificial satellites naturally tend to accumulate electrostatic charge which may in some circumstances cause malfunctions in measuring instruments and other devices on the satellite body and ultimately lead to difficulties in satellite operation. In this paper, we investigate the possibility of the use of the Lorentz force, which acts on charged satellite when it is moving through the magnetic field, as a means of satellite attitude control. We first analyze the stability of the motion and then propose novel attitude control method using the Lorentz force.. |

67. |
Mai Bando, Akira Ichikawa, Formation flying along a circular orbit with pulse control, AIAA/AAS Astrodynamics Specialist Conference 2010, 2010, This paper is concerned with formation flying along a circular orbit. The control input is of pulse type and the performance index is the total velocity change required for formation acquisition. For the in-plane motion, optimal three-pulse strategies which use control acceleration only in the flight direction are given under the condition that the difference of orbit size is relatively larger than that of drift velocity. If the inputs are restricted to the radial direction, only formation reconfiguration is possible and optimal two-pulse strategies are given. For the out-of-plane motion, the existence of optimal single pulse strategies is shown. Formation flying with feedback control is also considered. For the in-plane motion, suboptimal feedback controllers are designed with the help of null controllability with vanishing energy of the Hill-Clohessy-Wiltshire equations. Feedback controls restricted to flight direction are also designed, and the total velocity changes are compared with those of full control. Simulation results for a formation reconfiguration problem are given both for optimal open loop strategies and feedback controls.. |

68. |
Mai Bando, Akira Ichikawa, From elliptic restricted three-body problem to Tschauner-Hempel equations A control strategy based on circular problems, AAS/AIAA Astrodynamics Specialist Conference, 2010, This paper considers halo orbit control for the Earth-moon elliptic restricted threebody problem. Expressing equations of motion with true anomaly, Lagrangian points are defined and a halo orbit control problem at the L _{2} point is discussed. By the change of control variables, constant feedback controllers are designed which maintain a halo orbit of the circular restricted problem. Considering equations of motion relative to the moon, and letting the mass of the moon go to zero, the equations of relative motion along an eccentric orbit are derived. Then formation and reconfiguration problems are formulated, and feedback controllers, based on the Hill-Clohessy-Wiltshire systems, are designed from the point of view of L_{1}-norm minimization.. |

69. |
Mai Bando, Hiroshi Yamakawa, Low-thrust trajectory optimization using second-order generating functions, SICE Annual Conference 2010, SICE 2010, 2010, The optimal control problem of a spacecraft using continuous thrust where the terminal state and time interval are explicitly given is considered. We consider a new robust controller to the spacecraft rendezvous problem. Optimal rendezvous problem using continuous low-thrust is treated as optimal control problem and H_{∞} control. Using the property that both problems can be treated as two-point boundary value problem (TPVBP) of Hamiltonian system, we formulate the linear quadratic control with worst case disturbance rejection and worst case initial condition related by generating functions. Numerical simulations are given to illustrate the theory.. |

70. |
Mai Bando, Hiroshi Yamakawa, Near-Earth asteroid survey mission concept using solar sailing technology, 12th International Conference of Pacific-Basin Societies, ISCOPS, 2010, The purpose of this paper is to investigate the possibility of asteroid survey mission enabled by advanced solar sailing technology. The study is focused not on the solar sail spacecraft itself but on its orbital dynamics to realize the missions. A novel NEA flyby survey mission with a light-weight solar sail spacecraft to increase the accessibility to NEAs located in the vicinity of the Earth's orbit is proposed. Numerical study suggests that our approach increase the opportunities in proximity to NEAs which have eccentric and inclined orbits.. |

71. |
Mai Bando, Hiroshi Yamakawa, Solution to lambert's problem using generalized canonical transformations, AAS/AIAA Space Flight Mechanics Meeting, 2010, In this paper, we consider the canonical transformations and its applications appearing in astrodynamic problems. First we address stabilization of relative motion via generalized canonical transformation and passivity-based control. Then we propose a method to solve Lambert's problem based on the Hamilton-Jacobi-Bellman (HJB) equation in optimal control theory. Using the generalized canonical transformation, we transform the performance index to positive- definite one and then solve the optimal control problem. We also apply our method to obtain solution to two-point boundary-value problem by the generating function. As an application of the generating functions approach, we consider the problem of multiple flyby mission with impulsive thrust.. |

72. |
Mai Bando, Hiroshi Yamakawa, A new optimal orbit control for two-point boundary-value problem using generating functions, 19th AAS/AIAA Space Flight Mechanics Meeting, 2009, The optimal control problem of a spacecraft using impulsive and continuous thrust where the terminal state and time interval are explicitly given is considered. Using a recently developed technique based on Hamilton-Jacobi theory, we develop a method to approximate the solution of the Hamilton-Jacobi equation which can solve the two-point boundary-value problem. The proposed method is based on the successive approximation and Galerkin spectral method with Chebyshev polynomials. This approach is expected to derive the analytical solution of the optimal control problem in the large domain. Numerical simulation is given to illustrate the theory.. |

73. |
A. Ichikawa, Mai Bando, Satellite formation with restricted control interval, 2009 7th Asian Control Conference, ASCC 2009, 2009, In this paper, a formation problem of a satellite with a leader in an eccentric orbit is considered, where the transition to a periodic relative orbit is required, and the control input is restricted to a subinterval of the period of the leader's orbit. As preliminaries, the same problem in the special case of the circular orbit is considered, and feedback controls based on a differential Riccati equation with a periodic control matrix are designed. The performance index is the L_{1}-norm of the feedback control, and suboptimal controls are obtained by virtue of the null controllability with vanishing energy of the controlled system. Then the original problem is transformed into a special form by the change of variables, and using the structure of the resulting system, feedback controls are designed based on those of the circular problem.. |

74. |
Mai Bando, Akira Ichikawa, Adaptive output regulation of nonlinear systems described by multiple linear models, 9th IFAC Workshop "Adaptation and Learning in Control and Signal Processing", ALCOSP'2007, 2007.12, In this paper the output regulation problem for nonlinear systems described by multiple linear models with unknown parameters is considered. Based on the Lyapunov stability theory, an adaptive controller which stabilize the system is derived. Then sufficient conditions for the output regulation problem with full information to be solvable are established. Simulation results are given to illustrate the theory.. |

75. |
Mai Bando, Akira Ichikawa, Adaptive output regulation for linear systems, 2006 SICE-ICASE International Joint Conference, 2006, In this paper, the output regulation problem for linear time-invariant systems with unknown parameters is considered. Based on Lyapunov stability theorem, an adaptive controller which achieves regulation is derived. Then, sufficient conditions for the existence of a controller that solves the output regulation problem with state feedback are established and simulation result are given.. |

76. |
Mai Bando, Hiroaki Nakanishi, Koichi Inoue, A study on designing control system by modular learning, SICE Annual Conference 2004, 2004, A control system, which consists of several cooperative modules whose combination and structures change dynamically according to the state and environment, is discussed in this paper. We propose a method to design a control system by modular learning. Numerical simulations and flight experiment of an autonomous aero-robot demonstrate the effectiveness of the proposed method.. |