Nonlinear attitude control of spacecraft with strain-actuated solar arrays

This thesis presents a mathematical framework for precision attitude control of a spacecraft using the inertial coupling between the spacecraft and solar arrays. The spacecraft with solar arrays is modeled as a one degree of freedom cylinder (rigid body rotation) with flexible appendages (infinite-dimensional system). The equations of motion that describe system evolution are derived using the extend generalizations of the Lagrangian for infinite dimension systems. Precision attitude control is achieved by bending the flexible appendage using strain actuators. Global asymptotic convergence of the controller’s is proved using the Lyapunov direct method, which ensures that the control objectives of trajectory tracking and slewing are achieved. The Input-to-State stability of these controllers is used to generalize the control laws in terms of a variable that scales the stiffness term. The closed-loop system is simulated numerically for different values of the variable to verify stability. An experimental setup, that mimics a spacecraft with solar arrays is designed as a cylinder that is secured to a flexible beam using an interference fit. The strain actuation of the beam is achieved using piezoelectric actuators. The rotation of the cylinder and bending in beam are estimated using measurements from a Vicon motion capture system. The closed-loop system is tested in real-time to achieve controlled rotation of the cylinder

Trajectory Optimization for Chance-Constrained Nonlinear Stochastic Systems

This paper presents a new method of computing a sub-optimal solution of a continuous-time continuous-space chance-constrained stochastic nonlinear optimal control problem (SNOC) problem. The proposed method involves two steps. The first step is to derive a deterministic nonlinear optimal control problem (DNOC) with convex constraints that are surrogate to the SNOC by using generalized polynomial chaos (gPC) expansion and tools taken from chance-constrained programming. The second step is to solve the DNOC problem using sequential convex programming (SCP) for trajectory generation. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC because the gPC approximation of the random variables converges to the true distribution. The effectiveness of the gPC-SCP method is demonstrated by computing safe trajectories for a second-order planar robot model with multiplicative stochastic uncertainty entering at the input while avoiding collisions with a specified probability

Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an \underline{Info}rmation-cost \underline{S}tochastic \underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem (Info-SNOC). The optimization objective encodes both optimal performance and exploration for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.Comment: Submitted to RA-L 2020, review-

Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an Information-cost Stochastic Nonlinear Optimal Control problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach

Ultra-Soft Electromagnetic Docking with Applications to In-Orbit Assembly

Docking small satellites in space is a high-risk operation due to the uncertainty in relative position and orientation and the lack of mature docking technologies. This is particularly true for missions that involve multiple docking and undocking procedures like swarm-based construction and reconfiguration. In this paper, an electromagnetic docking system is proposed to mitigate these risks through robust, ultra-soft, propellant-free docking. Designed with reconfigurable self-assembly in mind, the gripping mechanism is androgynous, able to dock at a variety of relative orientations, and tolerant of small misalignments. The mechanical and control design of the system is presented and tested in both simulation and on a fleet of 6 degree-of-freedom (DOF) spacecraft simulators. The spacecraft simulators oat on the precision flat floor facility in the Caltech Aerospace Robotics and Control lab, the largest of its kind at any university. The performance of the electromagnetic docking system on-board the simulators is then compared against a propulsive docking system

Distributed multi-target relative pose estimation for cooperative spacecraft swarm

Multi-agent relative state estimation is critical in enabling full swarm autonomy. However, relative pose estimation of hundreds to thousands of cooperative agents is challenging due to limited sensing, limited communication, and scalability. We present a distributed algorithm for cooperative multi-agent localization with both limited relative sensing and communication. Each agent locally exchanges the relative measurements and jointly estimates the relative poses of its local neighbors. Because the algorithm only estimates the local neighbors, the number of states does not grow with the total number of agents given the same local sensing and communication graphs, making the algorithm suitable for swarm application. The proposed algorithm is applied to spacecraft swarm localization and verified in simulation and experiments. Experiments are conducted on Caltech’s robotic spacecraft simulators, the Multi-Spacecraft Testbed for Autonomy Research (M-STAR), where each spacecraft uses vision-based relative measurements