Swarm assignment and trajectory optimization using variable-swarm, distributed auction assignment and sequential convex programming

This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm

Guidance and control of swarms of spacecraft

There has been considerable interest in formation flying spacecraft due to their potential to perform certain tasks at a cheaper cost than monolithic spacecraft. Formation flying enables the use of smaller, cheaper spacecraft that distribute the risk of the mission. Recently, the ideas of formation flying have been extended to spacecraft swarms made up of hundreds to thousands of 100-gram-class spacecraft known as femtosatellites. The large number of spacecraft and limited capabilities of each individual spacecraft present a significant challenge in guidance, navigation, and control. This dissertation deals with the guidance and control algorithms required to enable the flight of spacecraft swarms. The algorithms developed in this dissertation are focused on achieving two main goals: swarm keeping and swarm reconfiguration. The objectives of swarm keeping are to maintain bounded relative distances between spacecraft, prevent collisions between spacecraft, and minimize the propellant used by each spacecraft. Swarm reconfiguration requires the transfer of the swarm to a specific shape. Like with swarm keeping, minimizing the propellant used and preventing collisions are the main objectives. Additionally, the algorithms required for swarm keeping and swarm reconfiguration should be decentralized with respect to communication and computation so that they can be implemented on femtosats, which have limited hardware capabilities. The algorithms developed in this dissertation are concerned with swarms located in low Earth orbit. In these orbits, Earth oblateness and atmospheric drag have a significant effect on the relative motion of the swarm. The complicated dynamic environment of low Earth orbits further complicates the swarm-keeping and swarm-reconfiguration problems. To better develop and test these algorithms, a nonlinear, relative dynamic model with $J_2$ and drag perturbations is developed. This model is used throughout this dissertation to validate the algorithms using computer simulations. The swarm-keeping problem can be solved by placing the spacecraft on J2-invariant relative orbits, which prevent collisions and minimize the drift of the swarm over hundreds of orbits using a single burn. These orbits are achieved by energy matching the spacecraft to the reference orbit. Additionally, these conditions can be repeatedly applied to minimize the drift of the swarm when atmospheric drag has a large effect (orbits with an altitude under 500 km). The swarm reconfiguration is achieved using two steps: trajectory optimization and assignment. The trajectory optimization problem can be written as a nonlinear, optimal control problem. This optimal control problem is discretized, decoupled, and convexified so that the individual femtosats can efficiently solve the optimization. Sequential convex programming is used to generate the control sequences and trajectories required to safely and efficiently transfer a spacecraft from one position to another. The sequence of trajectories is shown to converge to a Karush-Kuhn-Tucker point of the nonconvex problem. In the case where many of the spacecraft are interchangeable, a variable-swarm, distributed auction algorithm is used to determine the assignment of spacecraft to target positions. This auction algorithm requires only local communication and all of the bidding parameters are stored locally. The assignment generated using this auction algorithm is shown to be near optimal and to converge in a finite number of bids. Additionally, the bidding process is used to modify the number of targets used in the assignment so that the reconfiguration can be achieved even when there is a disconnected communication network or a significant loss of agents. Once the assignment is achieved, the trajectory optimization can be run using the terminal positions determined by the auction algorithm. To implement these algorithms in real time a model predictive control formulation is used. Model predictive control uses a finite horizon to apply the most up-to-date control sequence while simultaneously calculating a new assignment and trajectory based on updated state information. Using a finite horizon allows collisions to only be considered between spacecraft that are near each other at the current time. This relaxes the all-to-all communication assumption so that only neighboring agents need to communicate. Experimental validation is done using the formation flying testbed. The swarm-reconfiguration algorithms are tested using multiple quadrotors. Experiments have been performed using sequential convex programming for offline trajectory planning, model predictive control and sequential convex programming for real-time trajectory generation, and the variable-swarm, distributed auction algorithm for optimal assignment. These experiments show that the swarm-reconfiguration algorithms can be implemented in real time using actual hardware. In general, this dissertation presents guidance and control algorithms that maintain and reconfigure swarms of spacecraft while maintaining the shape of the swarm, preventing collisions between the spacecraft, and minimizing the amount of propellant used

Real-Time Optimal Control and Target Assignment for Autonomous In-Orbit Satellite Assembly from a Modular Heterogeneous Swarm

This paper presents a decentralized optimal guidance and control scheme to combine a heterogeneous swarm of component satellites, rods and connectors, into a large satellite structure. By expanding prior work on a decentralized auction algorithm with model predictive control using sequential convex programming (MPC-SCP) to allow for the limited type heterogeneity and docking ability required for in-orbit assembly. The assignment is performed using a distributed auction with a variable number of targets and strict bonding rules to address the heterogeneity. MPC-SCP is used to generate the collision-free trajectories, with modifications to the constraints to allow docking

Distributed Fast Motion Planning for Spacecraft Swarms in Cluttered Environments Using Spherical Expansions and Sequence of Convex Optimization Problems

This paper presents a novel guidance algorithm for spacecraft swarms in an environment cluttered with many obstacles like a debris field or the asteroid belt. The objective of this algorithm is to reconfigure the swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. The agents first use a spherical-expansion-based sampling algorithm to cooperatively explore the workspace and find paths to the desired terminal positions. Using a distributed assignment algorithm, the agents converge on an optimal assignment of the target locations in the desired formation. Then each agent generates a locally optimal trajectory from its current location to its terminal position by solving a sequence of convex optimization problems. As the agent moves along this trajectory, it receives the position of other agents and updates its trajectory to avoid collisions with other agents and the obstacles. Thus the swarm achieves the desired formation in a distributed manner while avoiding collisions. Moreover, this algorithm is computationally efficient, therefore it can be implemented onboard resource-constrained spacecraft. Simulations results show that the proposed distributed algorithm can be used by a spacecraft swarm to reconfigure a desired formation around an asteroid in a collision-free manner

Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments

This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments. In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE-SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE-SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agent and the moving obstacles. Simulations results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles

Autonomous In-Orbit Satellite Assembly from a Modular Heterogeneous Swarm

This paper presents a decentralized, distributed guidance and control scheme to combine a heterogeneous swarm of component satellites into a large satellite structure. The component satellites for the heterogeneous swarm are chosen to promote flexibility in final shape inspired by crystal structures and Islamic tile art. After the ideal fundamental building blocks are selected, basic nanosatellite-class satellite designs are made to assist in simulations involving attitude control. The Swarm Orbital Construction Algorithm (SOCA) is a guidance and control algorithm to allow for the limited type heterogeneity and docking ability required for in-orbit assembly. The algorithm consists of two parts, a distributed auction which uses barrier functions to ensure the proper agent selection for each target, and a trajectory generation portion which leverages model predictive control and sequential convex programming to achieve optimal collision-free trajectories to the desired target point even with nonlinear system dynamics. The optimization constraints use a boundary layer to determine whether the collision avoidance or the docking constraints should be applied. The algorithm was tested in a simulated perturbed 6-DOF spacecraft dynamic environment for planar and out-of-plane final structures and on two robotic platforms, including a swarm of frictionless spacecraft simulation robots

Real-Time Optimal Control and Target Assignment for Autonomous In-Orbit Satellite Assembly from a Modular Heterogeneous Swarm

This paper presents a decentralized optimal guidance and control scheme to combine a heterogeneous swarm of component satellites, rods and connectors, into a large satellite structure. By expanding prior work on a decentralized auction algorithm with model predictive control using sequential convex programming (MPC-SCP) to allow for the limited type heterogeneity and docking ability required for in-orbit assembly. The assignment is performed using a distributed auction with a variable number of targets and strict bonding rules to address the heterogeneity. MPC-SCP is used to generate the collision-free trajectories, with modifications to the constraints to allow docking

Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731