Modeling and High-Performance Algorithms for Mission-Constrained Trajectory Optimization

Abstract

Autonomous systems increasingly rely on optimization-based planning and control to achieve complex tasks while satisfying dynamics, actuator limitations, safety requirements, and mission objectives. As these systems are asked to operate in more demanding environments, two challenges become central. First, mission requirements must be modeled in a mathematically precise and optimization-compatible way. Second, the resulting nonconvex trajectory generation and guidance problems must be solved reliably and efficiently. This dissertation addresses both challenges through the joint development of modeling frameworks and high-performance algorithms for trajectory optimization with mission-level specifications, together with a decentralized Markov-chain synthesis framework for swarm guidance. The first part of the dissertation develops a common numerical optimal-control backbone based on free-final-time formulations, time-dilation, finite-dimensional control parameterization, multiple-shooting discretization, and exact-penalty finite-dimensional transcriptions. Building on this foundation, the dissertation develops smooth and exact modeling tools for mission-level specifications using generalized mean-based smooth robustness (GMSR). At the logical level, the resulting constructions provide $\mathcal{C}^1$-smooth and exact parameterizations of temporal logic operators. At the temporal level, the framework is extended from discrete-time STL to continuous-time STL through two complementary realizations: a dense-time realization that is sound and complete up to the accuracy of the underlying numerical integration scheme, and an augmentation-based realization that embeds temporal aggregation directly into augmented dynamics and is particularly attractive for implementation. These constructions avoid the locality and masking behavior of standard quantitative semantics and yield a more favorable landscape for gradient-based optimization. To solve the resulting optimization problems, the dissertation develops prox-convex, a structure-preserving sequential convex programming algorithm for composite problems in which convex penalties act on smooth features and smooth outer maps act on convex inner features. Each prox-convex step linearizes only the smooth maps while preserving the available convex structure, and the method is equipped with adaptive proximal regularization, optional curvature injection, and convergence guarantees that include sufficient decrease, complexity bounds, and local linear convergence under a local error-bound condition. The modeling and algorithmic ingredients are then integrated in a range of trajectory optimization applications, including illustrative continuous-time STL examples, nonlinear model predictive control with continuous-time constraint satisfaction, perception-constrained motion planning for information acquisition, rocket landing with compound state-triggered constraints, and quadrotor flight with continuous-time STL requirements. The dissertation also addresses large-scale distributed guidance through decentralized state-dependent Markov-chain synthesis (DSMC). A state-dependent consensus protocol is first developed and shown to achieve exponential convergence under mild technical conditions without relying on conventional connectivity assumptions on the dynamic graph topology. Building on this protocol, the dissertation develops a decentralized Markov-chain synthesis method that converges exponentially to a desired steady-state distribution while respecting transition constraints and reducing unnecessary state transitions. Its effectiveness is demonstrated on probabilistic swarm-guidance problems, where it achieves substantially faster convergence than existing Markov-chain-based methods. Taken together, the results of this dissertation provide a unified perspective on how expressive modeling and structure-preserving algorithms can be combined to enable reliable and efficient guidance for both individual autonomous vehicles and large-scale swarms.