Pseudospectral Knotting Methods for Solving Optimal Control Problems

The article of record as published may be found at https://doi.org/10.2514/1.3426A class of computational methods for solving a wide variety of optimal control problems is presented; these problems include nonsmooth, nonlinear, switched optimal control problems, as well as standard multiphase prob lems. Methods are based on pseudospectral approximations of the differential constraints that are assumed to be given in the form of controlled differential inclusions including the usual vector field and differential-algebraic forms. Discontinuities and switches in states, controls, cost functional, dynamic constraints, and various other mappings associated with the generalized Bolza problem are allowed by the concept of pseudospectral (PS) knots. Information across switches and corners is passed in the form of discrete event conditions localized at the PS knots. The optimal control problem is approximated to a structured sparse mathematical programming problem. The discretized problem is solved using off-the-shelf solvers that include sequential quadratic programming and interior point methods. Two examples that demonstrate the concept of hard and soft knots are presented.Charles Stark Draper Laboratory, Inc. (Draper)Jet Propulsion Laboratory (JPL)Naval Postgraduate SchoolSecretary of the U.S. Air Forc

Which Way Was I Going? Contextual Retrieval Supports the Disambiguation of Well Learned Overlapping Navigational Routes

Groundbreaking research in animals has demonstrated that the hippocampus contains neurons that distinguish betweenoverlapping navigational trajectories. These hippocampal neurons respond selectively to the context of specific episodes despite interference from overlapping memory representations. The present study used functional magnetic resonanceimaging in humans to examine the role of the hippocampus and related structures when participants need to retrievecontextual information to navigate well learned spatial sequences that share common elements. Participants were trained outside the scanner to navigate through 12 virtual mazes from a ground-level first-person perspective. Six of the 12 mazes shared overlapping components. Overlapping mazes began and ended at distinct locations, but converged in the middle to share some hallways with another maze. Non-overlapping mazes did not share any hallways with any other maze. Successful navigation through the overlapping hallways required the retrieval of contextual information relevant to thecurrent navigational episode. Results revealed greater activation during the successful navigation of the overlapping mazes compared with the non-overlapping mazes in regions typically associated with spatial and episodic memory, including thehippocampus, parahippocampal cortex, and orbitofrontal cortex. When combined with previous research, the current findings suggest that an anatomically integrated system including the hippocampus, parahippocampal cortex, and orbitofrontal cortexis critical for the contextually dependent retrieval of well learned overlapping navigational routes

Time-Optimal Nonlinear Feedback Control for the NPSAT1 Spacecraft, IEEE-ASME (2005; Monterey, California)

The article of record as published may be located at http://ieeexplore.ieee.orgProceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics ; Monterey, California, USA, 24-28 July, 2005NPSAT1 is a small satellite being built at the Naval Postgraduate School, and due to launch in January 2006. It uses magnetic actuators and a pitch momentum wheel for attitude control. In this paper, a novel time-optimal sampled-data feedback control algorithm is introduced for closed-loop control of NPSAT1 in the presence of disturbances. The feedback law is not analytically explicit; rather, it is obtained by a rapid re-computation of the open-loop time-optimal control at each update instant. The implementation of the proposed controller is based on a shrinking horizon approach and does not require any advance knowledge of the computation time. The ground- test simulations show that the proposed control scheme performs well in the presence of parameter uncertainties and external disturbance torques.NAApproved for public release; distribution is unlimited

A Pseudospectral Optimal Motion Planner for Autonomous Unmanned Vehicles

2010 American Control Conference, Marriott Waterfront, Baltimore, MD, USA, June 30-July 02, 2010This paper presents a pseudospectral (PS) optimal control algorithm for the autonomous motion planning of a fleet of unmanned ground vehicles (UGVs). The UGVs must traverse an obstacle-cluttered environment while maintaining robustness against possible collisions. The generality of the algorithm comes from a binary logic that modifies the cost function for various motion planning modes. Typical scenarios including path following and multi-vehicle pursuit are demonstrated. The proposed framework enables the availability of real-time information to be exploited by real-time reformulation of the optimal control problem combined with real-time computation. This allows the each vehicle to accommodate potential changes in the mission/environment and uncertain conditions. Experimental results are presented to substantiate the utility of the approach on a typical planning scenario

Design and Control of Libration Point Spacecraft Formations

The article of record as published may be located at http://dx.doi.org/10.2514/6.2004-4786Proceedings of AIAA Guidance, Navigation, and Control Conference ; Paper no. AIAA 2004-4786, Providence, Rhode Island, Aug. 16-19 2004We investigate the concurrent problem of orbit design and formation control around a libration point. The problem formulation is based on a framework of multi-agent, nonlinear optimal control. The optimality criterion is fuel consumption modeled as the L1-norm of the control acceleration. Fuel budgets are allocated by isoperimetric constraints. The nonsmooth optimal control problem is discredited using DIDO, a software package that implements the Legendre pseudospectral method. The discretized problem is solved using SNOPT, a sequential quadratic programming solver. Among many, one of the advantages of our approach is that we do not require linearization or analytical results; consequently, the inherent nonlinearities associated with the problem are automatically exploited. Sample results for formations about the Sun-Earth L2 point in the 3-body circular restricted dynamical framework are presented. Globally optimal solutions for relaxed and almost periodic formations are presented for both a large separation constraint (about a third to half of orbit size), and a small separation constraint (a few hundred km or about 5_10_6 of orbit size).N

Hippocampus and retrosplenial cortex combine path integration signals for successful navigation

The current study used fMRI in humans to examine goal-directed navigation in an open field environment. We designed a task that required participants to encode survey-level spatial information and subsequently navigate to a goal location in either first person, third person, or survey perspectives. Critically, no distinguishing landmarks or goal location markers were present in the environment, thereby requiring participants to rely on path integration mechanisms for successful navigation. We focused our analysis on mechanisms related to navigation and mechanisms tracking linear distance to the goal location. Successful navigation required translation of encoded survey-level map information for orientation and implementation of a planned route to the goal. Our results demonstrate that successful first and third person navigation trials recruited the anterior hippocampus more than trials when the goal location was not successfully reached. When examining only successful trials, the retrosplenial and posterior parietal cortices were recruited for goal-directed navigation in both first person and third person perspectives. Unique to first person perspective navigation, the hippocampus was recruited to path integrate self-motion cues with location computations toward the goal location. Last, our results demonstrate that the hippocampus supports goal-directed navigation by actively tracking proximity to the goal throughout navigation. When using path integration mechanisms in first person and third person perspective navigation, the posterior hippocampus was more strongly recruited as participants approach the goal. These findings provide critical insight into the neural mechanisms by which we are able to use map-level representations of our environment to reach our navigational goals

On the Pseudospectral Convector Mapping Theorem for Nonlinear Optimal Control, IEEE (45th; 2006)

The article of record as published may be located at http://ieeexplore.ieee.orgProceedings of 45th IEEE Conference on Decision and Control Page(s): 2679 - 2686, Dec.13-15, 2006In recent years, a large number of nonlinear optimal control problems have been solved by pseudospectral (PS) methods. In an effort to better understand the PS approach to solving control problems, we present convergence results for problems with mixed state and control constraints. A set of sufficient conditions are proved under which the solution of the discretized optimal control problem converges to the continuous solution. Conditions for the convergence of the duals are described and illustrated. This leads to a clarification of covector mapping theorem and its connections to constraint qualifications.Approved for public release; distribution is unlimited

Friction of Wheat: Grain-on-Grain and on Corrugated Steel

Coefficients of friction of wheat for grain–on–grain and on galvanized corrugated steel sheet were investigated using a modified direct shear apparatus. Tests were conducted under a normal pressure of 20.7 kPa using soft red winter wheat at a moisture content of 11.2% (w.b.) and an uncompressed bulk density of 740 kg/m3. Three consolidation procedures and three methods of deposition of grain in the test chamber were used. Test results of grain–on–grain friction showed that consolidation procedure markedly influenced the force–displacement relationship, while its influence on the coefficients of friction were small. Shearing to peak strength as a consolidation method erased all effects of loading history and resulted in the highest values of the coefficient of friction. Grain–on–grain coefficients of friction were in a range from 0.47 ± 0.007 to 0.56 ± 0.004 depending on the method of grain deposition. Friction on two dimensionally different samples of corrugated steel sheet was examined using three methods of grain deposition. Corrugation depths were 13 mm on both samples, while their periods were 67.5 mm (short) and 104 mm (long). Coefficients of friction on the short–period corrugated samples were in a range from 0.42 ± 0.0 to 0.46 ± 0.004 and were significantly higher (α = 5%) than those on the long–period corrugated sample, which ranged from 0.36 ± 0.003 to 0.39 ± 0.003. The method of grain deposition significantly (α = 5%) influenced the coefficients of friction of wheat on both types of corrugated steel sheet

The Programmer's Assistant: Conversational Interaction with a Large Language Model for Software Development

Large language models (LLMs) have recently been applied in software engineering to perform tasks such as translating code between programming languages, generating code from natural language, and autocompleting code as it is being written. When used within development tools, these systems typically treat each model invocation independently from all previous invocations, and only a specific limited functionality is exposed within the user interface. This approach to user interaction misses an opportunity for users to more deeply engage with the model by having the context of their previous interactions, as well as the context of their code, inform the model's responses. We developed a prototype system -- the Programmer's Assistant -- in order to explore the utility of conversational interactions grounded in code, as well as software engineers' receptiveness to the idea of conversing with, rather than invoking, a code-fluent LLM. Through an evaluation with 42 participants with varied levels of programming experience, we found that our system was capable of conducting extended, multi-turn discussions, and that it enabled additional knowledge and capabilities beyond code generation to emerge from the LLM. Despite skeptical initial expectations for conversational programming assistance, participants were impressed by the breadth of the assistant's capabilities, the quality of its responses, and its potential for improving their productivity. Our work demonstrates the unique potential of conversational interactions with LLMs for co-creative processes like software development.Comment: 43 pages, 3 figures. To be published in IUI 202

Packing Factors of Feed Products in Storage Structures

Experiments were conducted to measure the changes in bulk density of cracked corn, corn meal, soybean meal, cotton seed meal, and distillers dried grain (without solubles) when subjected to simulated overburden pressures. All materials were tested at two moisture content levels (approximately 8% and 12% w.b.) and seven pressures between 0 and 69 kPa (0 and 10 psi). A mathematical model was fitted to the data to predict the bulk density of each feed ingredient as a function of pressure and moisture content. These relationships were inserted into a previously developed computer model to predict ingredient packing within conventional storage structures based on Janssen\u27s equation as a function of feed product type, moisture content of the material, friction characteristics of the bin wall material, material height, and bin diameter. Cracked corn experienced the smallest amount of packing (approximately 4.3% in a bin with a diameter of 1.8 m and a height of 1.8 m), while distillers dried grain (without solubles) had approximately 8.1% packing in the same sized bin. With a bin diameter of 5.5 m and a height of 5.5 m, distillers dried grain (without solubles) and cracked corn had a packing factor of 13.3% and 6.8%, respectively. As moisture content increased the amount of packing increased for all materials. The data presented can be used for inventory control and management