Generalized conflict learning for hybrid discrete/linear optimization

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 73-76).Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. In many of these applications there is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal solution. In the arena of model-based autonomy, discrete systems, like deep space probes, have given way to more agile systems, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear and non-linear as well as logical constraints. This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, generalizing from the conflict-directed search algorithms of model-based reasoning. We introduce a novel algorithm called Generalized Conflict-directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or sub-optimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. We evaluate GCD-BB empirically on a range of test problems of coordinated air vehicle control. GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm, applied to either disjunctive linear programs or an equivalent binary integer program encoding.by Hui Li.S.M

Chance-Constrained Optimal Path Planning With Obstacles

Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. For robust execution, we must take into account uncertainty, which arises due to uncertain localization, modeling errors, and disturbances. Prior work handled the case of set-bounded uncertainty. We present here a chance-constrained approach, which uses instead a probabilistic representation of uncertainty. The new approach plans the future probabilistic distribution of the vehicle state so that the probability of failure is below a specified threshold. Failure occurs when the vehicle collides with an obstacle or leaves an operator-specified region. The key idea behind the approach is to use bounds on the probability of collision to show that, for linear-Gaussian systems, we can approximate the nonconvex chance-constrained optimization problem as a disjunctive convex program. This can be solved to global optimality using branch-and-bound techniques. In order to improve computation time, we introduce a customized solution method that returns almost-optimal solutions along with a hard bound on the level of suboptimality. We present an empirical validation with an aircraft obstacle avoidance example.National Science Foundation (U.S.) (Grant IIS-1017992)Boeing Company (Grant MIT-BA-GTA-1

Coordinating Agile Systems through the Model-based Execution of Temporal Plans

SM thesisAgile autonomous systems are emerging, such as unmanned aerial vehicles (UAVs), that must robustly perform tightly coordinated time-critical missions; for example, military surveillance or search-and-rescue scenarios. In the space domain, execution of temporally flexible plans has provided an enabler for achieving the desired coordination and robustness, in the context of space probes and planetary rovers, modeled as discrete systems. We address the challenge of extending plan execution to systems with continuous dynamics, such as air vehicles and robot manipulators, and that are controlled indirectly through the setting of continuous state variables.Systems with continuous dynamics are more challenging than discrete systems, because they require continuous, low-level control, and cannot be controlled by issuing simple sequences of discrete commands. Hence, manually controlling these systems (or plants) at a low level can become very costly, in terms of the number of human operators necessary to operate the plant. For example, in the case of a fleet of UAVs performing a search-and-rescue scenario, the traditional approach to controlling the UAVs involves providing series of close waypoints for each aircraft, which incurs a high workload for the human operators, when the fleet consists of a large number of vehicles.Our solution is a novel, model-based executive, called Sulu, that takes as input a qualitative state plan, specifying the desired evolution of the state of the system. This approach elevates the interaction between the human operator and the plant, to a more abstract level where the operator is able to Âcoach the plant by qualitatively specifying the tasks, or activities, the plant must perform. These activities are described in a qualitative manner, because they specify regions in the plantÂs state space in which the plant must be at a certain point in time. Time constraints are also described qualitatively, in the form of flexible temporal constraints between activities in the state plan. The design of low-level control inputs in order to meet this abstract goal specification is then delegated to the autonomous controller, hence decreasing the workload per human operator. This approach also provides robustness to the executive, by giving it room to adapt to disturbances and unforeseen events, while satisfying the qualitative constraints on the plant state, specified in the qualitative state plan.Sulu reasons on a model of the plant in order to dynamically generate near-optimal control sequences to fulfill the qualitative state plan. To achieve optimality and safety, Sulu plans into the future, framing the problem as a disjunctive linear programming problem. To achieve robustness to disturbances and maintain tractability, planning is folded within a receding horizon, continuous planning and execution framework. The key to performance is a problem reduction method based on constraint pruning. We benchmark performance using multi-UAV firefighting scenarios on a real-time, hardware-in-the-loop testbed

Collaborative Diagnosis of Over-Subscribed Temporal Plans

PhD thesisOver-subscription, that is, being assigned too many tasks or requirements that are too demanding, is commonly encountered in temporal planning problems. As human beings, we often want to do more than we can, ask for things that may not be available, while underestimating how long it takes to perform each task. It is often difficult for us to detect the causes of failure in such situations and then find resolutions that are effective. We can greatly benefit from tools that assist us by looking out for these plan failures, by identifying their root causes, and by proposing preferred resolutions to these failures that lead to feasible plans. In recent literature, several approaches have been developed to resolve such over-subscribed problems, which are often framed as over-constrained scheduling, configuration design or optimal planning problems. Most of them take an all-or-nothing approach, in which over-subscription is resolved through suspending constraints or dropping goals. While helpful, in real-world scenarios, we often want to preserve our plan goals as much possible. As human beings, we know that slightly weakening the requirements of a travel plan, or replacing one of its destinations with an alternative one is often sufficient to resolve an over-subscription problem, no matter if the requirement being weakened is the duration of a deep-sea survey being planned for, or the restaurant cuisine for a dinner date. The goal of this thesis is to develop domain independent relaxation algorithms that perform this type of slight weakening of constraints, which we will formalize as continuous relaxation, and to embody them in a computational aid, Uhura, that performs tasks akin to an experienced travel agent or ocean scientists. In over-subscribed situations, Uhura helps us diagnose the causes of failure, suggests alternative plans, and collaborates with us in order to resolve conflicting requirements in the most preferred way. Most importantly, the algorithms underlying Uhura supports the weakening, instead of suspending, of constraints and variable domains in a temporally flexible plan. The contribution of this thesis is two-fold. First, we developed an algorithmic framework, called Best-first Conflict-Directed Relaxation (BCDR), for performing plan relaxation. Second, we use the BCDR framework to perform relaxation for several different families of plan representations involving different types of constraints. These include temporal constraints, chance constraints and variable domain constraints, and we incorporate several specialized conflict detection and resolution algorithms in support of the continuous weakening of them. The key idea behind BCDR's approach to continuous relaxation is to generalize the concepts of discrete conflicts and relaxations, first introduced by the model-based diagnosis community, to hybrid conflicts and relaxations, which denote minimal inconsistencies and minimal relaxations to both discrete and continuous relaxable constraints

Generative planner for hybrid systems with temporally extended goals

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 230-237).Most unmanned missions in space and undersea are commanded by a "script" that specifies a sequence of discrete commands and continuous actions. Currently such scripts are mostly hand-generated by human operators. This introduces inefficiency, puts a significant cognitive burden on the engineers, and prevents re-planning in response to environment disturbances or plan execution failure. For discrete systems, the field of autonomy has elevated the level of commanding by developing goal-directed systems, to which human operators specify a series of temporally extended goals to be accomplished, and the goal-directed systems automatically output the correct, executable command sequences. Increasingly, the control of autonomous systems involves performing actions with a mix of discrete and continuous effects. For example, a typical autonomous underwater vehicle (AUV) mission involves discrete actions, like get GPS and take sample, and continuous actions, like descend and ascend, which are influenced by the dynamical model of the vehicle. A hybrid planner generates a sequence of discrete and continuous actions that achieve the mission goals. In this thesis, I present a novel approach to solve the generative planning problem for temporally extended goals for hybrid systems, involving both continuous and discrete actions. The planner, Kongming, incorporates two innovations. First, it employs a compact representation of all hybrid plans, called a Hybrid Flow Graph, which combines the strengths of a Planning Graph for discrete actions and Flow Tubes for continuous actions. Second, it engages novel reformulation schemes to handle temporally flexible actions and temporally extended goals. I have successfully demonstrated controlling an AUV in the Atlantic ocean using mission scripts solely generated by Kongming. I have also empirically evaluated Kongming on various real-world scenarios in the underwater domain and the air vehicle domain, and found it successfully and efficiently generates valid and optimal plans.by Hui X. Li.Ph.D

Kongming: A Generative Planner for Hybrid Systems with Temporally Extended Goals

PhD thesisMost unmanned missions in space and undersea are commanded by a "script" that specifies a sequence of discrete commands and continuous actions. Currently such scripts are mostly hand-generated by human operators. This introduces inefficiency, puts a significant cognitive burden on the engineers, and prevents re-planning in response to environment disturbances or plan execution failure. For discrete systems, the field of autonomy has elevated the level of commanding by developing goal-directed systems, to which human operators specify a series of temporally extended goals to be accomplished, and the goal-directed systems automatically output the correct, executable command sequences. Increasingly, the control of autonomous systems involves performing actions with a mix of discrete and continuous effects. For example, a typical autonomous underwater vehicle (AUV) mission involves discrete actions, like get GPS and take sample, and continuous actions, like descend and ascend, which are influenced by the dynamical model of the vehicle. A hybrid planner generates a sequence of discrete and continuous actions that achieve the mission goals. In this thesis, I present a novel approach to solve the generative planning problem for temporally extended goals for hybrid systems, involving both continuous and discrete actions. The planner, Kongming, incorporates two innovations. First, it employs a compact representation of all hybrid plans, called a Hybrid Flow Graph, which combines the strengths of a Planning Graph for discrete actions and Flow Tubes for continuous actions. Second, it engages novel reformulation schemes to handle temporally flexible actions and temporally extended goals. I have successfully demonstrated controlling an AUV in the Atlantic ocean using mission scripts solely generated by Kongming. I have also empirically evaluated Kongming on various real-world scenarios in the underwater domain and the air vehicle domain, and found it successfully and efficiently generates valid and optimal plans.Funded by the Boeing Company under contract MIT-BA-GTA-

Multistate analysis and design : case studies in aerospace design and long endurance systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, September 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections."September 2011." Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 221-230).This research contributes to the field of aerospace engineering by proposing and demonstrating an integrated process for the early-stage, multistate design of aerospace systems. The process takes into early consideration the many partially degraded states that real-world systems experience throughout their operation. Despite advancing efforts aimed at maintaining operation in a state of optimum performance, most systems spend very substantial amounts of time operating in degraded or off-nominal states (e.g. Hubble space telescope, Mars Spirit rover, or aircraft flying under minimum-equipment-list restrictions). There exist relatively few methods and tools to address this at the beginning of the design process. At one end of the spectrum is design optimization, but this typically concentrates on the system in its nominal state of operation, only infrequently considering failure states through piecemeal application of constraints. There is reliability analysis, which focuses on component failure rates and the benefits of redundancy but does not consider how well or poorly the system performs with partial failures. Finally, there is controls theory, where control laws are optimized but the plant is typically assumed to be given a priori. The methodology described within this thesis coordinates elements from each of these three areas into an effective integrated framework. It allows the designer deeper insight into the complex problem of designing cost effective systems that must operate for long durations with little or expensive opportunity for repair or intervention. Specific contributions include: 1) the above methodology, which evaluates responses in system expected performance and availability to changes in static design variables (geometry) and component failure rates, accounting for control design variables (gains) where appropriate, 2) the demonstration of the cost and benefits associated with a multistate design approach as compared to reliability analysis and the nominal design approach, and 3) a multilayer extension of Markov analysis, for translating single sortie vehicle level metrics into measures of multistate campaign performance. The process is demonstrated through three application case studies. The first of these establishes the feasibility of the approach through the multistate analysis of performance for an existing twin-engine aircraft. This analysis was enabled through the development of a multidisciplinary simulation based design model for evaluation of multistate aircraft performance. A medium-altitude long endurance unmanned aerial vehicle is designed in the second case study, first from a single-sortie, ultra long endurance perspective and then from a multiple sortie, mission campaign perspective. Finally, the third case study demonstrates applicability of the approach to a lower level subsystem, that of the lubrication system for a geared turbofan engine. Several major findings result from these case studies, including that: 1) multistate performance output spaces have distinctly unique shapes and boundaries, depending on whether formed through variation of component failure rates, static design variables (geometry), or a multistate combination of both, 2) a region of multistate performance results from the combined variation of failure rates and static design variables that is unachievable through the independent variation of either one, 3) small changes in static design variables may be used to significantly improve system availability, and 4) the general multistate design problem is one of competing objectives between system availability, expected performance, nominal performance, and cost.by Jeremy S. Agte.Ph.D

Robust, goal-directed plan execution with bounded risk

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 273-283).There is an increasing need for robust optimal plan execution for multi-agent systems in uncertain environments, while guaranteeing an acceptable probability of success. For example, a fleet of unmanned aerial vehicles (UAVs) and autonomous underwater vehicles (AUVs) are required to operate autonomously for an extensive mission duration in an uncertain environment. Previous work introduced the concept of a model-based executive, which increases the level of autonomy, elevating the level at which systems are commanded. This thesis develops model-based executives that reason explicitly from a stochastic plant model to find the optimal course of action, while ensuring that the probability of failure is within a user-specified risk bound. This thesis presents two robust mode-based executives: probabilistic Sulu or p-Sulu, and distributed probabilistic Sulu or dp-Sulu. The objective for p-Sulu and dp-Sulu is to allow users to command continuous, stochastic multi-agent systems in a manner that is both intuitive and safe. The user specifies the desired evolution of the plant state, as well as the acceptable probabilities of failure, as a temporal plan on states called a chance-constrained qualitative state plan (CCQSP). An example of a CCQSP statement is "go to A through B within 30 minutes, with less than 0.001% probability of failure." p-Sulu and dp-Sulu take a CCQSP, a continuous plant model with stochastic uncertainty, and an objective function as inputs, and outputs an optimal continuous control sequence, as well as an optimal discrete schedule. The difference between p-Sulu and dp-Sulu is that p-Sulu plans in a centralized manner while dp-Sulu plans in a distributed manner. dp-Sulu enables robust CCQSP execution for multi-agent systems. We solve the problem based on the key concept of risk allocation, which achieves tractability by allocating the specified risk to individual constraints and mapping the result into an equivalent deterministic constrained optimization problem. Risk allocation also enables a distributed plan execution for multi-agent systems by distributing the risk among agents to decompose the optimization problem. Building upon the risk allocation approach, we develop our first CCQSP executive, p-Sulu, in four spirals. First, we develop the Convex Risk Allocation (CRA) algorithm, which can solve a CCQSP planning problem with a convex state space and a fixed schedule, highlighting the capability of optimally allocating risk to individual constraints. Second, we develop the Non-convex Iterative Risk Allocation (NIRA) algorithm, which can handle non-convex state space. Third, we build upon NIRA a full-horizon CCQSP planner, p-Sulu FH, which can optimize not only the control sequence but also the schedule. Fourth, we develop p-Sulu, which enables the real-time execution of CCQSPs by employing the receding horizon approach. Our second CCQSP executive, dp-Sulu, is developed in two spirals. First, we develop the Market-based Iterative Risk Allocation (MIRA) algorithm, which can control a multiagent system in a distributed manner by optimally distributing risk among agents through the market-based method called tatonnement. Second and finally, we integrate the capability of MIRA into p-Sulu to build the robust model-based executive, dp-Sulu, which can execute CCQSPs on multi-agent systems in a distributed manner. Our simulation results demonstrate that our executives can efficiently execute CCQSP planning problems with significantly reduced suboptimality compared to prior art.by Masahiro Ono.Ph.D

Generalized conflict learning for hybrid discrete/linear optimization

Abstract. Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. At the core of many of these applications is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal feasible solution. In the arena of model-based autonomy, deep space probes have given way to more agile vehicles, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear as well as logical constraints. This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, carried from the conflict-directed search algorithm in model-based reasoning. We introduce a novel algorithm called Generalized Conflict-Directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or suboptimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. Evaluated empirically on a range of test problems of coordinated air vehicle control, GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm applied to either disjunctive linear programs or an equivalent binary integer programming encoding.