About

John Carson is an Associate Professor in the Department of History at the University of Michigan, with an office located in 1765 Haven Hall. He earned his Ph.D. from Princeton University in 1994. His research focuses on U.S. intellectual and cultural history, the history of science, the history of the human sciences, 19th-century U.S. history, and European intellectual history. Carson has contributed to the understanding of how modern democracies have balanced their commitment to equality with concerns about natural disparities in talent and intelligence. His notable work, 'The Measure of Merit,' explores how American and French societies have historically understood and managed human inequalities in relation to merit, talent, and intelligence, analyzing political, philosophical, scientific, and journalistic writings over two centuries. His scholarship provides insights into the social and political implications of scientific ideas about human abilities and inequalities.

Research topics

• Computer Science
• Artificial Intelligence
• Mathematical optimization
• Mathematics
• Algorithm
• Aerospace engineering
• Engineering
• Mathematical analysis

Selected publications

• Active Continuous-Time Simultaneous Localization & Mapping for Powered Descent Guidance Maneuvers

  2026-01-08

  article

  The problem of guidance-navigation co-design for autonomous aerospace systems concerns the simultaneous satisfaction of guidance and navigation requirements in mission & trajectory design, and is of keen interest for the realization of robust autonomy in the aerospace industry. In this paper, a general-purpose technique–Active Continuous-Time Simultaneous Localization & Mapping (ACTSLAM)–is proposed to systematically and flexibly solve for various elements of guidance-navigation co-design and is specialized for scenarios involving spatial perception objectives. The resulting architecture makes use of advances in successive convexification for nonconvex trajectory optimization to solve the resulting problem at near-real-time speeds. ACT-SLAM is consequently demonstrated on the highly-constrained powered descent guidance (PDG) problem in a lunar environment with LiDAR-based measurements, showing promising results for joint reduction in vehicle and mapping uncertainty. Furthermore, rigorous satisfaction of both guidance and navigation requirements is shown through 3σ Monte Carlo analysis, and benchmark comparisons to several recent methods are made, demonstrating considerable improvements in terms of information-theoretic objectives.

  PublisherDOI

• Auto-Tuned Successive Convexification for Entry Guidance With Continuous-Time Constraint Satisfaction

  2026-01-08

  article

  In this work, we present an auto-tuning hypersonic entry guidance framework that enforces continuous-time constraint satisfaction. In this study, we merge two existing methodologies–AutoSCvx for penalty-weight autotuning and CT-SCvx for continuous-time constraint enforcement–into a unified successive convexification framework: CT-AutoSCvx. This combination removes the need for dense temporal grids, mesh refinement, or manually tuned penalty weights. The resulting algorithm provides three key capabilities for reentry trajectory optimization: (1) continuous-time satisfaction of nonlinear path constraints, (2) automatic tuning of the virtual-buffer penalties associated with the augmented constraints, and (3) treatment of time-interval dilation as an augmented control input. Numerical results are presented for a conceptual human-scale Mars entry vehicle.

  PublisherDOI

• Sequential Convex Programming for 6-DoF Powered Descent Guidance With Continuous-time Compound State-Triggered Constraints

  2025-01-03 · 5 citations

  articleSenior author

  This paper presents a sequential convex programming (SCP) framework for ensuring the continuous-time satisfaction of compound state-triggered constraints, a subset of temporal specifications, in the powered descent guidance (PDG) problem. The proposed framework combines the generalized mean-based smooth robustness measure (D-GMSR), a parameterization technique tailored for expressing temporal and logical specifications through smooth functions, with the continuous-time successive convexification (CT-SCvx) method, a real-time solution for constrained trajectory optimization that guarantees continuous-time constraint satisfaction and convergence. The smoothness of the temporal and logical specifications parameterized via D-GMSR enables solving the resulting optimization problem with robust and efficient SCP algorithms while preserving theoretical guarantees. In addition to their smoothness, the parameterized specifications are sound and complete, meaning the specification holds if and only if the constraint defined by the parameterized function is satisfied. The CT-SCvx framework is then applied to solve the parameterized problem, incorporating: (1) reformulation for continuous-time path constraint satisfaction, (2) time-dilation to transform the free-final-time PDG problem into a fixed-final-time problem, (3) multiple shooting for exact discretization, (4) exact penalty functions for penalizing nonconvex constraints, and (5) the prox-linear method, a convergence-guaranteed SCP algorithm, to solve the resulting finite-dimensional nonconvex PDG problem. The effectiveness of the framework is demonstrated through numerical simulations. The implementation is available at https://github.com/UW-ACL/CT-cSTC

  PublisherDOI

• Information-Aware Powered Descent Guidance for Entry, Descent and Landing

  2025-01-03 · 1 citations

  articleSenior author

  In many autonomous navigation tasks, agents must make decisions based on perceptual information. Enhancing information gain from observations enables agents to achieve goals more efficiently, especially in time- and fuel-critical situations like Powered Descent Guidance. This paper proposes a trajectory optimization framework that promotes information maximization. We employ Gaussian process regression to model the landing space topography, providing surface estimates and their covariance. This covariance integral is used as a cost in an SCP-based trajectory optimization problem, allowing the agent to plan trajectories that minimize environmental covariance. We demonstrate our algorithm in a high-fidelity simulation using Unreal Engine with Digital Elevation Models captured by the Lunar Reconnaissance Orbiter.

  PublisherDOI

• Continuous-Time Line-of-Sight Constrained Trajectory Planning for 6-Degree of Freedom Systems

  IEEE Robotics and Automation Letters · 2025-02-24 · 1 citations

  article

  Perception algorithms are ubiquitous in modern autonomy stacks, providing necessary environmental information to operate in the real world. Many of these algorithms depend on the visibility of keypoints, which must remain within the robot's line-of-sight (LoS) for reliable operation. This letter tackles the challenge of maintaining LoS on such keypoints during robot movement. We propose a novel method that addresses these issues by ensuring applicability to various sensor footprints, adaptability to arbitrary nonlinear system dynamics, and constant enforcement of LoS throughout the robot's path. Our experiments show that the proposed approach achieves significantly reduced LoS violation and runtime compared to existing state-of-the-art methods in several representative and challenging scenarios.

  PublisherDOI

• Implementation and Testing of Convex Optimization-based Guidance for Hazard Detection and Avoidance on a Lunar Lander

  2024-01-04 · 9 citations

  article

  Lunar logistics companies have experienced growth over the past few years, with interest focused on delivering payloads to hazardous areas like the South Pole. Achieving safe touchdowns while meeting precise landing requirements necessitates more and more advanced perception sensor suites and in-situ data collection of the environments. One such sensor includes hazard detection LIDARs, which typically constrain trajectories to meet specific range, velocity, time, and field of view requirements for data collection. Creating a real-time guidance solution to meet these constraints has motivated past research on solvers that use convex formulations and embed these constraints directly in the problem formulation. Maturation of these approaches has in turn motivated the testing and implementation for use in-flight and onboard a lander. While more advanced 6-DOF approaches exist, 3-DOF formulations are attractive due to their simpler implementation and faster solve times. In this paper, a 3-DOF solution for meeting convex hazard detection and avoidance constraints is presented, followed by implementation and 6-DOF testing results for both a software-in-the-loop Monte Carlo platform and a real-time hardware-in-the-loop flight processor platform. In addition, a novel constraint formulation is introduced, known as the control-robust envelope, which enables guaranteed satisfaction of hazard detection objectives. Results show that the implementation approach works in both meeting the trajectory constraints for hazard detection and avoidance and is achievable in real-time on the flight platform.

  PublisherDOI

• Constrained Visibility Guidance for Terrain Scanning using 6-DOF Sequential Convex Programming

  2024-01-04 · 5 citations

  article

  Recent advances in perceptive sensors and computer vision have motivated new formulations for powered descent guidance, wherein a vehicle must perform a pinpoint landing on a celestial body while simultaneously conducting close-range scans of the landing environment to detect and avoid potentially-unsafe hazards. Furthermore, mission plans may necessitate exploration and scouting of the environment to determine candidate landing sites in real time. In this paper, a novel six degree-of-freedom (6-DOF) optimal control formulation is presented to model visibility-based constraints such that line-of-sight to a circular ground-based region of interest is guaranteed, up to a specified discrete temporal resolution, with an accommodating theory of constrained conic intersections introduced to support this approach. This formulation, termed Constrained Visibility Guidance (CVG), further leverages and extends theory in sequential convex programming and state-triggered constraints to enable mission-practical constraint specification and transformation of a highly-nonconvex problem into one that can be iteratively solved with modern second-order cone program solvers. Ultimately, CVG is shown to be highly performant in terms of solve time and convergence properties, even under complex and highly-constrained problem design. Numerical simulation results are presented to validate these claims.

  PublisherDOI

• Continuous-Time Line-of-Sight Constrained Trajectory Planning for 6-Degree of Freedom Systems

  arXiv (Cornell University) · 2024-10-29 · 1 citations

  preprintOpen access

  Perception algorithms are ubiquitous in modern autonomy stacks, providing necessary environmental information to operate in the real world. Many of these algorithms depend on the visibility of keypoints, which must remain within the robot's line-of-sight (LoS), for reliable operation. This paper tackles the challenge of maintaining LoS on such keypoints during robot movement. We propose a novel method that addresses these issues by ensuring applicability to various sensor footprints, adaptability to arbitrary nonlinear system dynamics, and constant enforcement of LoS throughout the robot's path. Our experiments show that the proposed approach achieves significantly reduced LoS violation and runtime compared to existing state-of-the-art methods in several representative and challenging scenarios.

  PublisherOA PDFDOI

• Real-Time Sequential Conic Optimization for Multi-Phase Rocket Landing Guidance

  IFAC-PapersOnLine · 2023-01-01 · 31 citations

  articleOpen accessCorresponding

  We introduce a multi-phase rocket landing guidance framework that can handle nonlinear dynamics and does not mandate any additional mixed-integer or nonconvex constraints to handle discrete temporal events/switching. To achieve this, we first introduce sequential conic optimization (seco), a new paradigm for solving nonconvex optimal control problems that is entirely devoid of matrix factorizations and inversions. This framework combines sequential convex programming (SCP) and first-order conic optimization and can solve unified multi-phase trajectory optimization problems in real-time. The novel features of this framework are: (1) time-interval dilation, which enables multi-phase trajectory optimization with free-transition-time; (2) single-crossing compound state-triggered constraints, which are entirely convex if the trigger and constraint conditions are convex; (3) virtual state, which is a new approach to handling artificial infeasibility in SCP methods that preserves the shapes of the constraint sets; and, (4) the use of the proportional-integral projected gradient method (pipg), a high-performance first-order conic optimization solver, in tandem with the penalized trust region (ptr) SCP algorithm. We demonstrate the efficacy and real-time capability of seco by solving a relevant multi-phase rocket landing guidance problem with nonlinear dynamics and convex constraints only, and observe that our solver is 2.7 times faster than a state-of-the-art convex optimization solver.

  PublisherDOI

• Customized Real-Time First-Order Methods for Onboard Dual Quaternion-based 6-DoF Powered-Descent Guidance

  AIAA SCITECH 2023 Forum · 2023-01-19 · 30 citations

  article

  View Video Presentation: https://doi.org/10.2514/6.2023-2003.vid The dual quaternion-based 6-DoF powered-descent guidance algorithm (DQG) was selected as the candidate powered-descent guidance algorithm for NASA’s Safe and Precise Landing — Integrated Capabilities Evolution (SPLICE) project. DQG is capable of handling state-triggered constraints that are of the utmost importance in terms of enabling technologies such as terrain relative navigation (TRN). In this work, we develop a custom solver for DQG to enable onboard implementation for future rocket landing missions. We describe the design and implementation of a real-time-capable optimization framework, called sequential conic optimization (SeCO), that blends together sequential convex programming and first-order conic optimization to solve difficult nonconvex trajectory optimization problems, such as DQG, in real-time. This framework is entirely devoid of matrix factorizations/inversions, making it suitable for safety-critical applications. Under the hood, the SeCO framework leverages a first-order primal-dual conic optimization solver, based on the proportional-integral projected gradient method (PIPG), that combines the ideas of projected gradient descent and proportional-integral feedback of constraint violation. Unlike other conic optimization solvers, PIPG effectively exploits the sparsity and geometric structure of the constraints, avoids expensive equation solving, and is suitable for both real-time and large-scale applications. We describe the implementation of this solver, and develop customizable first-order methods, including an analytical preconditioning algorithm, to solve the nonconvex DQG optimal control problem in real-time. Strategies such as warm-starting and extrapolation are leveraged to further accelerate convergence. We show that the DQG-customized solver is able to solve the problem significantly faster than other state-of-the-art convex optimization solvers, and thus demonstrate the viability of SeCO for real-time, mission-critical applications onboard computationally constrained flight hardware.

  PublisherDOI

Frequent coauthors

• Behçet Açıkmeşe

  American Institute of Aeronautics and Astronautics

  47 shared

• John N. Kandara

  37 shared

• Amy C. Christensen

  37 shared

• Farzin Amzajerdian

  21 shared

• Mehran Mesbahi

  15 shared

• Carolina Restrepo

  Goddard Space Flight Center

  14 shared

• Glenn D. Hines

  14 shared

• Taylor P. Reynolds

  Amazon (United States)

  13 shared

Education

• PhD, History

  Princeton University

  1993