Mark B. Milam

A new computational approach to real-time trajectory generation for constrained mechanical systems

Preliminary results of a new computational approach to generate aggressive trajectories in real-time for constrained mechanical systems are presented. The algorithm is based on a combination of the nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that real-time trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the nonlinear trajectory generation software package.

Inversion Based Constrained Trajectory Optimization

Abstract A computationally efficient technique for the numerical solution of optimal control problems is discussed. This method utilizes tools from nonlinear control theory to transform the optimal control problem to a new, lower dimensional set of coordinates. It is hypothesized that maximizing the relative degree in this transformation is directly related to minimizing the computation time. Firm evidence of this hypothesis is given by numerical experiments. Results are presented using the Nonlinear Trajectory Generation (NTG) software package.

Applied receding horizon control of the Caltech Ducted Fan

This paper details the application of a constrained receding horizon control strategy to an indoor vectored-thrust flight experiment known as the Caltech Ducted Fan. The strategy is used to stabilize the experiment about one operating point, and step response and disturbance rejection are examined with different configurations and in comparison to a gain-scheduled LQR controller. Issues related to non-zero computation times, choice of horizon length and terminal cost are discussed.

REAL-TIME CONSTRAINED TRAJECTORY GENERATION APPLIED TO A FLIGHT CONTROL EXPERIMENT

Abstract A computational approach to generate real-time, optimal trajectories for a flight control experiment is presented. Minimum time trajectories are computed for hover-to-hover and forward flight maneuvers. Instantaneous changes in the trajectory constraints that model obstacles and threats are also investigated. Experimental results using the Nonlinear Trajectory Generation software package show good closed-loop performance for all maneuvers. Success of the algorithm demonstrates that high-confidence real-time trajectory generation is achievable in spite of the highly nonlinear and non-convex nature of the problem.

MODEL PREDICTIVE CONTROL OF A THRUST-VECTORED FLIGHT CONTROL EXPERIMENT

Abstract Model predictive control (MPC) is applied to the Caltech ducted fan, a thrust-vectored flight experiment. A real-time trajectory generation software based on spline theory and sequential quadratic programming is used to implement the MPC controllers. Timing issues related to the computation and implementation of repeatedly updated optimal trajectories are discussed. Results show computational speeds greater than 10 Hz, 2.5 times that of the actuator dynamics. The MPC controllers successfully stabilize a step disturbance applied to the ducted fan and compare favorably to LQR methods.

CONSTRAINED TRAJECTORY GENERATION FOR MICRO-SATELLITE FORMATION FLYING

Station-keeping and reorientation control ofa cluster off ully-actuated low-thrust micro-satellites is considered in this paper. We propose a very general optimization based control methodology to solve constrained trajectory generation problems for stationkeeping and reorientation. By taking advantage ofthe f ully-actuated structure ofthe micro-satellite, it is possible to compute the control on-board the micro-satellites. Performance of this methodology is reported for a typical micro-satellite formation flying space mission using the Nonlinear Trajectory Generation software package.

A testbed for nonlinear flight control techniques: the Caltech ducted fan

This paper considers the fundamental design and modeling of the Caltech ducted fan. The Caltech ducted fan is a scaled model of the longitudinal axis of a flight vehicle. The purpose of the ducted fan is the research and development of new nonlinear flight guidance and control techniques for uninhabited combat aerial vehicles. It is shown that critical design relations must be satisfied in order that the ducted fans longitudinal dynamics behave similar to those of an flight vehicle. Preliminary flight test results illustrate the flying qualities of the ducted fan.

Passively safe Receding Horizon Control for satellite proximity operations

Recent on-orbit mission performance illustrates a pressing need to develop passively safe formation flight trajectories and controllers for multiple satellite proximity operations. A receding horizon control (RHC) approach is formulated that directly relates navigation uncertainty and process noise to non-convex quadratic constraints, which enforce passive safety in the presence of a large class of navigation or propulsion system failures. Several Keplerian simulations are executed to examine increased ¿v usage incurred by adding passive safety constraints, the corresponding reduction in collision probability, and resulting passively safe formation flight geometries. Results show that modest cross-track motion significantly reduces collision probability, and that once a passively safe relative orbit is achieved, steady-state ¿v usage rates are comparable to usage rates without passive safety constraints. Navigation uncertainty and process noise are found to be significant ¿v usage drivers for passively safe proximity operations. Onorbit autonomous RHC control with passive safety constraints applied to proximity operation missions enables trajectory generation and control that reduces collision probability to acceptable levels while minimizing ¿v usage.

A NEW COMPUTATIONAL METHOD FOR OPTIMAL CONTROL OF A CLASS OF CONSTRAINED SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS

Abstract A computationally efficient technique for the numerical solution of constrained optimal control problems governed by one-dimensional partial differential equations is considered in this paper. This technique utilizes inversion to map the optimal control problem to a lower dimensional space. Results are presented using the Nonlinear Trajectory Generation software package (NTG) showing that real-time implementation may be possible.

Proximity Operations Testing with a Rotating and Translating Resident Space Object

Hardware-In-The-Loop (HWIL) test results using guidance, navigation, and control software to perform the proximity operations between a noncooperative rotating and translating Resident Space Object (RSO) and an Agile Space Vehicle (ASV) are presented. The HWIL test cases employ an unknown RSO to demonstrate RSO feature identication, insitu accurate three-dimensional RSO model construction, constrained optimal guidance, and relative navigation sensor processing algorithms. The real-time HWIL proximity operations demonstration was performed at the Naval Research Laboratory Space Robotics Facility using representative space-qualied hardware. Results from the six-degree-of-freedom testing showed that accurate proximity operations can be performed with a rotating and translating noncooperative RSO.