John M. Carson

Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem

Planetary soft landing is one of the benchmark problems of optimal control theory and is gaining renewed interest due to the increased focus on the exploration of planets in the solar system, such as Mars. The soft landing problem with all relevant constraints can be posed as a finite-horizon optimal control problem with state and control constraints. The real-time generation of fuel-optimal paths to a prescribed location on a planets surface is a challenging problem due to the constraints on the fuel, the control inputs, and the states. The main difficulty in solving this constrained problem is the existence of nonconvex constraints on the control input, which are due to a nonzero lower bound on the control input magnitude and a nonconvex constraint on its direction. This paper introduces a convexification of the control constraints that is proven to be lossless; i.e., an optimal solution of the soft landing problem can be obtained via solution of the proposed convex relaxation of the problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain optimal solutions of the original nonconvex optimal control problem.

A model predictive control technique with guaranteed resolvability and required thruster silent times for small-body proximity operations

The guidance and control algorithms for enabling spacecraft proximity operations about small celestial bodies are developed by using a model predictive control approach. Separate feedforward and feedback components are utilized. The feedforward, or open-loop, guidance is based on a pseudo way-point generation algorithm that uses a discrete linear-timevarying model of the dynamics that incorporates required thruster silent times. This leads to a convex formulation of the open-loop trajectory generation problem with control and state constraints. Particularly, the pseudo way-points are generated through the solution of a second-order cone programming problem (a subclass of semi-definite programming), and there are interior point methods to compute the global optimum with a deterministic stopping criteria and a prescribed level of accuracy. Feedback control is implemented to track the pseudo way-point trajectories in a manner that guarantees the resolvability for the open-loop problem, enabling the ability to update the guidance profile in a robust, model-predictive manner. The robust guidance and control algorithm with resolvability is demonstrated in the simulation of a spacecraft landing onto a small asteroid possessing a significant gravity field; incorporating a gravity model into the algorithm provides notable improvements in controller performance.

A robust model predictive control algorithm augmented with a reactive safety mode

A reactive safety mode is built into a robust model predictive control algorithm for uncertain nonlinear systems with bounded disturbances. The algorithm enforces state and control constraints and blends two modes: (I) standard, guarantees re-solvability and asymptotic convergence in a robust receding-horizon manner; (II) safety, if activated, guarantees containment within an invariant set about a reference. The reactive safety mode provides robustness to unexpected, but real-time anticipated, state-constraint changes during standard mode operation. The safety-mode control policy is designed offline and can be activated at any arbitrary time. The standard-mode control has feedforward and feedback components: feedforward is from online solution of a finite-horizon optimal control problem; feedback is designed offline to provide robustness to system uncertainty and disturbances and to establish an invariant “state tube” that guarantees standard-mode re-solvability at any time. The algorithm design is shown for a class of systems with incrementally-conic uncertain/nonlinear terms and bounded disturbances.

A hybrid FPGA/Tilera compute element for autonomous hazard detection and navigation

To increase safety for future missions landing on other planetary or lunar bodies, the Autonomous Landing and Hazard Avoidance Technology (ALHAT) program is developing an integrated sensor for autonomous surface analysis and hazard determination. The ALHAT Hazard Detection System (HDS) consists of a Flash LIDAR for measuring the topography of the landing site, a gimbal to scan across the terrain, and an Inertial Measurement Unit (IMU), along with terrain analysis algorithms to identify the landing site and the local hazards. An FPGA and Manycore processor system was developed to interface all the devices in the HDS, to provide high-resolution timing to accurately measure system state, and to run the surface analysis algorithms quickly and efficiently. In this paper, we will describe how we integrated COTS components such as an FPGA evaluation board, a TILExpress64, and multi-threaded/multi-core aware software to build the HDS Compute Element (HDSCE). The ALHAT program is also working with the NASA Morpheus Project and has integrated the HDS as a sensor on the Morpheus Lander. This paper will also describe how the HDS is integrated with the Morpheus lander and the results of the initial test flights with the HDS installed. We will also describe future improvements to the HDSCE.

Flight Testing a Real-Time Hazard Detection System for Safe Lunar Landing on the Rocket-Powered Morpheus Vehicle

The Hazard Detection System (HDS) is a component of the ALHAT (Autonomous Landing and Hazard Avoidance Technology) sensor suite, which together provide a lander Guidance, Navigation and Control (GN&C) system with the relevant measurements necessary to enable safe precision landing under any lighting conditions. The HDS consists of a stand-alone compute element (CE), an Inertial Measurement Unit (IMU), and a gimbaled flash LIDAR sensor that are used, in real-time, to generate a Digital Elevation Map (DEM) of the landing terrain, detect candidate safe landing sites for the vehicle through Hazard Detection (HD), and generate hazard-relative navigation (HRN) measurements used for safe precision landing. Following an extensive ground and helicopter test campaign, ALHAT was integrated onto the Morpheus rocket-powered terrestrial test vehicle in March 2014. Morpheus and ALHAT then performed five successful free flights at the simulated lunar hazard field constructed at the Shuttle Landing Facility (SLF) at Kennedy Space Center, for the first time testing the full system on a lunar-like approach geometry in a relevant dynamic environment. During these flights, the HDS successfully generated DEMs, correctly identified safe landing sites and provided HRN measurements to the vehicle, marking the first autonomous landing of a NASA rocket-powered vehicle in hazardous terrain. This paper provides a brief overview of the HDS architecture and describes its in-flight performance.

Real-Time Hazard Detection and Avoidance Demonstration for a Planetary Lander

The Autonomous Landing Hazard Avoidance Technology (ALHAT) Project is chartered to develop and mature to a Technology Readiness Level (TRL) of six an autonomous system combining guidance, navigation and control with terrain sensing and recognition functions for crewed, cargo, and robotic planetary landing vehicles. In addition to precision landing close to a pre-mission defined landing location, the ALHAT System must be capable of autonomously identifying and avoiding surface hazards in real-time to enable a safe landing under any lighting conditions. This paper provides an overview of the recent results of the ALHAT closed loop hazard detection and avoidance flight demonstrations on the Morpheus Vertical Testbed (VTB) at the Kennedy Space Center, including results and lessons learned. This effort is also described in the context of a technology path in support of future crewed and robotic planetary exploration missions based upon the core sensing functions of the ALHAT system: Terrain Relative Navigation (TRN), Hazard Detection and Avoidance (HDA), and Hazard Relative Navigation (HRN).

Toward improved landing precision on Mars

Mars landers to date have flown ballistic entry trajectories with no trajectory control after the final maneuver before entry. 12Improvements in landing accuracies (from ∼150 km from the target for Mars Pathfinder to ∼30–40 km for MER and Phoenix) have been driven by approach navigation improvements. MSL will fly the first guided-entry trajectory to Mars, further improving accuracy to ∼10–12 km from the target. For future missions, landing within ∼100m is desired to assure landing safety close to a target of high scientific interest in irregular terrain, or to land near a previously landed asset. Improvements in approach navigation alone are not sufficient to achieve this requirement. If approach navigation error and IMU error are eliminated, the dominant error source is wind drift on the parachute, with map-tie error also significant. Correcting these errors requires terrain-relative navigation (TRN), which can be accomplished with passive imaging supplemented by radar for terrain sensing (with onboard navigation capable of processing measurements from IMU, imaging, and radar). Additionally, near-optimal-ΔV powered descent guidance is needed to minimize the amount of propellant required to reach the target. The capability to land within 100m can be applied in different landing modes depending on how much fuel is carried.

A nonlinear model predictive control algorithm with proven robustness and resolvability

A robustly stabilizing MPC (model predictive control) algorithm with guaranteed resolvability is developed for uncertain nonlinear systems. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feedforward; and (ii) feedback. Feedforward control and the associated nominal trajectory are obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line, based on a bound on the model uncertainty. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided

Optimal nonlinear guidance with inner-loop feedback for hypersonic re-entry

Development of feasible G&C (guidance and control) methods for precision atmospheric re-entry has remained a challenge since pre-Apollo-era space exploration. The inherent difficulty arises from the governing hypersonic dynamics being significantly nonlinear, subject to parametric uncertainty, and limited with control authority. Vehicle safety requirements impose further constraints, and desired cost objectives complicate an already difficult G&C problem. The scope of this paper is to present a guidance algorithm for optimal trajectory generation based on a reduced-dimension reentry formulation. Preliminary simulations demonstrate the algorithm with feedback used to track the guidance trajectory in the presence of initial state uncertainty. The objective is to further this approach toward an onboard receding-horizon implementation

Flight Testing ALHAT Precision Landing Technologies Integrated Onboard the Morpheus Rocket Vehicle

A suite of prototype sensors, software, and avionics developed within the NASA Autonomous precision Landing and Hazard Avoidance Technology (ALHAT) project were terrestrially demonstrated onboard the NASA Morpheus rocket-propelled Vertical Testbed (VTB) in 2014. The sensors included a lidar-based Hazard Detection System (HDS), a Navigation Doppler Lidar (NDL) velocimeter, and a long-range Laser Altimeter (LAlt) that enable autonomous and safe precision landing of robotic or human vehicles on solid solar system bodies under varying terrain lighting conditions. The flight test campaign with the Morpheus VTB involved a detailed integration and functional verification process, followed by tether testing and six successful free flights, including one night flight. The ALHAT sensor measurements were combined within a specialized ALHAT Navigation filter that was employed in closed-loop flight testing within the Morpheus Guidance, Navigation and Control (GN&C) subsystem. Flight testing on Morpheus utilized ALHAT for safe landing site identification and ranking, followed by precise surface-relative navigation to the selected landing site. The successful autonomous, closed-loop flight demonstrations of the prototype ALHAT system have laid the foundation for the infusion of safe, precision landing capabilities into future planetary exploration missions.