Unsik Lee

Constrained consensus via logarithmic barrier functions

In this paper, we consider distributed algorithms for consensus of multiple agents in presence of convex state constraints on individual agent state. Each agents state is assumed to be constrained in a distinct compact convex set. We show that following the proposed distributed protocol, the agents are guaranteed to reach an agreement on a state that lies at the intersection of individual convex constraint sets. This is accomplished by introducing and sharing auxiliary variables in the network. The auxiliary variable utilizes a logarithmic barrier function to form a convex potential that is augmented to the consensus protocol. The consensus algorithm is then interpreted as a gradient-descent algorithm which operates with the desire to reach consensus while avoiding violation of the constraint sets. This modified consensus algorithm is applicable when each agent is required to satisfy its own constraints while synchronizing with others, e.g., attitude synchronization in presence of attitude constraints. An example is given for two different network topologies to evaluate the effectiveness and the convergence rate of the proposed algorithm.

Spacecraft reorientation in presence of attitude constraints via logarithmic barrier potentials

This paper proposes a methodology-based on convex navigation functions-for three-axis attitude reorientation for a rigid body spacecraft in presence of multiple constraints. In this direction, two types of attitude constrained zones are first defined, namely, the attitude forbidden and mandatory zones. The paper then utilizes a convex parameterization of forbidden and mandatory zones for constructing a logarithmic barrier potential function that is subsequently used for the synthesis of the attitude control laws. The feasible controller which uses the feedback of the unit quaternions in the context of the proposed methodology is then implemented using a modified integrator back stepping method in order to compromise the actuator saturations. The paper concludes with a set of simulation results in order to evaluate the effectiveness, and demonstrate the viability, of the proposed methodology.

Feedback control for spacecraft reorientation under attitude constraints via convex potentials

A novel guidance algorithm is proposed for the attitude reorientation of a rigid body spacecraft in the presence of multiple types of attitude-constrained zones. In this direction, two types of attitude-constrained zones are first developed using unit quaternions, namely, the attitude-forbidden and -mandatory zones. The paper then utilizes a convex parameterization of forbidden and mandatory zones for constructing a strictly convex logarithmic barrier potential that is subsequently used for the synthesis of feedback attitude control laws while the inevitable unwinding phenomenon is given a simple and effective remedy. Model-independent and model-dependent control laws are then implemented by using the Lyapunov direct method and the modified integrator backstepping method. The paper concludes with a set of simulation results to evaluate the effectiveness and demonstrate the viability of the proposed methodology.

Optimal path planning for solar-powered UAVs based on unit quaternions

In this paper, we examine a unit quaternion based method to design the optimal paths with maximum sun exposure for unmanned aerial vehicles (UAVs) equipped with photovoltaic cells on their wings. The mission of traveling between two specified boundary points with fixed flying time and constant speed is considered. Since the solar power is the sole source of energy for these UAVs during the flight, we consider the problem of maximizing the incoming solar radiation throughout their trajectory. As the attitude of the UAV directly determines solar intensity normal to the vertical surface of the wing, we use a unit quaternion based method to control the attitude maneuver during the flight interval. Subsequently, the aircraft kinematics are expressed as quadratic functions in terms of unit quaternions which can be solved by a branch and bound approach. Simulation results in two and three dimensions are presented.

Constrained Autonomous Precision Landing via Dual Quaternions and Model Predictive Control

The problem of powered descent guidance and control for autonomous precision landing for next-generation planetary missions is addressed. The precision landing algorithm aims to trace a fuel-optimal trajectory while keeping geometrical constraints such as the line of sight to the target site. The design of an autonomous control algorithm managing such mission scenarios is challenging due to fact that critical geometrical constraints are coupled with the translational and rotational motions of the lander spacecraft, leading to a complex motion-planning problem. This problem is approached within the model predictive control framework by representing the dynamics of the rigid body in a uniform gravity field via a piecewise affine system taking advantage of the unit dual-quaternion parameterization. Such a parameterization in turn enables a six-degree-of-freedom motion planning in a unified framework while also admitting a quadratic cost on the required control commands to minimize propellant consumption. A n...

Distributed Motion Estimation of Space Objects Using Dual Quaternions

This paper examines the motion estimation problem for space objects using multiple image sensors in a connected network. The objective is to increase the estimation precision of relative translational and rotational motions based on integrated dual quaternion representations and cooperation between connected sensors. The relative motion of space objects is rst formulated using dual elements to express its kinematics and dynamics. Two modular optimization approaches, namely dual decomposition and distributed Newton methods, for decomposing this cooperative estimation problem among the sensors is then proposed. Simulation results from single sensor estimation and two distributed estimation frameworks are provided and compared.

Optimal Power Descent Guidance with 6-DoF Line of Sight Constraints via Unit Dual Quaternions

In this paper, we present a model predictive control (MPC) approach for powered descent guidance and control synthesis in the presence of line of sight and glide slope constraints. The design of an autonomous control algorithm for such a mission scenario is challenging due to fact that the constraints are coupled with rotational and translational motions of a lander spacecraft, leading to a complex configuration space. We approach this problem by representing the general dynamics of the rigid body in an uniform gravity field as a piece-wise affine system utilizing the unit dual quaternion parameterization. Such a parameterization enables a 6-DOF motion prediction algorithm while also allowing selecting a quadratic cost on the required acceleration commands in order to minimize propellant consumption. The constraints are imposed to ensure that the lander’s position and orientation are not violating the constraints. A novel feature of this approach is the development of convex representable subset of unit dual quaternions that correspond to translational and rotational states satisfying predefined types of constraints with respect to a moving body frame. The stability and feasibility issues of the piece-wise affine MPC approach are also discussed. Simulation results are then presented to demonstrate the effectiveness of the proposed algorithm for powered descent guidance.

Spacecraft synchronization in the presence of attitude constrained zones

In this paper, we consider the problem of achieving identical orientation for a group of spacecraft in presence of attitude forbidden zones. The attitude forbidden zones can be identically defined over the group of spacecraft or can be defined independently. In order to find a feasible consensus-like algorithm, we utilize the quadratic convex parameterization for the attitude forbidden zones with unit quaternions. Subsequently, we embed this parameterization into a convex auxiliary system-whose output is shared among the spacecraft through a communication network. The auxiliary systems output play the role of an indicator function for the spacecraft dynamics such that it does not violate the attitude forbidden zones while attempting to reach consensus. In order to evaluate the effectiveness of the algorithm, we present two sets of simulations where synchronization of six spacecraft with identical and independent attitude forbidden zones with random initial attitudes are considered.

Dual quaternions, rigid body mechanics, and powered-descent guidance

In this paper, we present a Lyapunov-based framework for the analysis of unconstrained and constrained coupled rotational and translational control problems. Autonomous control algorithms for constrained coupled rotational and translational motions are challenging to design as they involve dependent variables that evolve in distinct configuration spaces. In the meantime, the unit dual quaternion parameterization can capture this dependency. Using this parameterization, we develop an array of globally stable control laws for unconstrained and constrained rigid body dynamics via a convex energy like Lyapunov function on dual quaternions. Furthermore, we characterize the convex representable subset of unit dual quaternions that corresponds to translational and rotational states that satisfy a predefined field of view constraints with respect to the body frame. We then proceed to construct a convex logarithmic barrier function on these constrained sets, which is subsequently used for the synthesis of the translational and rotational control laws for a wide range of applications. Powered-descent guidance problem is discussed as a potential application for the proposed framework.

Fast inertia property estimation via convex optimization for the asteroid redirect mission

Accurate inertia property estimation is critical to the success of the upcoming asteroid redirect mission. The inertia tensor, center of mass, and total mass of the spacecraft-asteroid combined rigid body must be accurately estimated so that solar electric propulsion can be used to redirect an asteroid into an orbit around the Earth. This paper develops an efficient algorithm to solve for those properties. The estimation is framed as a least squares minimization problem subject to convex constraints. A standard least squares approach is not sufficient due to a matrix rank deficiency arising from the fact that a pure torque cannot be applied to the asteroid after capture. The constrained least squares minimization framework allows for fast inertia estimation with a convex optimization solver, in the sense that accurate estimates can be made with only a few force inputs and response measurements. Simulations are performed in MATLAB R2013B using the CVX 2.1 convex optimization solver to assess the algorithms performance in a typical mission scenario.