arXiv subjects

Naoya Kumagai

Publications and source records attributed to Naoya Kumagai.

6 recordsLinked to original sources

arXiv2026

On the Optimality of Markovian Policies for Chance-Constrained Covariance Steering

Many studies on finite-horizon stochastic optimal control, including covariance steering, parameterize control policies as state-history-affine. This parameterization enables a convex reformulation, thereby yielding a tractable solution method. However, the necessity of dependence on previous states has not been well established. \textit{Is this dependence necessary, or merely an artifact of the convex reformulation?} We show that it is an artifact that can be removed losslessly. Given an optimal solution of the state-history-affine formulation, we construct a deterministic Markovian policy which is affine in the current state. We show that, even for the covariance steering problem with a broad class of commonly used state and control safety constraints, the synthesized Markovian policy almost surely produces the same control actions as the history-dependent policy and therefore the same state trajectories, cost, and moments. Thus, every optimum of the history-dependent formulation admits a lossless Markovian transformation. Geometrically, the history-dependent formulation lifts the policy space for convexity, and its optimal solution can be projected back to the Markovian policy space. We extend the analysis to output feedback and a convex upper-bounding surrogate for value-at-risk costs.

math.OC↗

arXiv2026

Square Root-Factorized Covariance Steering

Covariance steering (CS) synthesizes a control policy which drives the state's mean and covariance matrix towards desired values. Offering tractable computation of a closed-loop policy which can obey chance constraints in uncertain environments, application to many real-world control problems have been proposed. We consider the chance-constrained, discrete-time, linear time-varying CS with Gaussian noise. The contribution of this paper is a novel solution method for this problem, explicitly writing the propagation equations of the Cholesky factor of the state covariance matrix by using the QR decomposition. The use of the square-root form of covariance matrices brings two key benefits over other existing methods: (i) computational scalability and (ii) numerical reliability. (i) Compared to solution methods that require large block matrix formulations, the proposed method scales better with the growth in horizon length, shows better optimality, and uses memoryless state feedback. (ii) Compared to another class of methods that explicitly define the covariance matrix as variables, the proposed method allows flexible cost formulations and shows better numerical reliability when uncertainty terms are smaller than the mean. On the other hand, these benefits come with a minor drawback: the propagation equation of covariance square roots is non-convex, necessitating sequential convex programming to solve. However, this paper proves the global optimality of the proposed approach for CS without chance constraints. When chance constraints are present, the existing optimal CS formulation is also non-convex, and we prove that the proposed approach shares the same local minima. We verify the mathematical arguments via extensive numerical simulations.

math.OC↗

arXiv2025

Hands-Off Covariance Steering: Inducing Feedback Sparsity via Iteratively Reweighted $\ell_{1,p}$ Regularization

We consider the problem of optimally steering the state covariance matrix of a discrete-time linear stochastic system to a desired terminal covariance matrix, while inducing the control input to be zero over many time intervals. We propose to induce sparsity in the feedback gain matrices by using a sum-of-norms version of the iteratively reweighted $\ell_1$-norm minimization. We show that the lossless convexification property holds even with the regularization term. Numerical simulations show that the proposed method produces a Pareto front of transient cost and sparsity that is not achievable by a simple $\ell_1$-norm minimization and closely approximates the $\ell_0$-norm minimization obtained from brute-force search.

math.OC↗

arXiv2025

Robust Cislunar Low-Thrust Trajectory Optimization under Uncertainties via Sequential Covariance Steering

Spacecraft operations are influenced by uncertainties such as dynamics modeling, navigation, and maneuver execution errors. Although mission design has traditionally incorporated heuristic safety margins to mitigate the effect of uncertainties, particularly before/after crucial events, it is yet unclear whether this practice will scale in the cislunar region, which features locally chaotic nonlinear dynamics and involves frequent lunar flybys. This paper applies chance-constrained covariance steering and sequential convex programming to simultaneously design an optimal trajectory and trajectory correction policy that can probabilistically guarantee safety constraints under the assumed physical/navigational error models. The results show that the proposed method can effectively control the state uncertainty in a highly nonlinear environment. The framework allows faster computation and lossless convexification of linear covariance propagation compared to existing methods, enabling a rapid and accurate comparison of $ΔV_{99}$ costs for different uncertainty parameters. We demonstrate the algorithm on several transfers in the Earth-Moon Circular Restricted Three Body Problem.

math.OC↗

arXiv2024

Chance-Constrained Gaussian Mixture Steering to a Terminal Gaussian Distribution

We address the problem of finite-horizon control of a discrete-time linear system, where the initial state distribution follows a Gaussian mixture model, the terminal state must follow a specified Gaussian distribution, and the state and control inputs must obey chance constraints. We show that, throughout the time horizon, the state and control distributions are fully characterized by Gaussian mixtures. We then formulate the cost, distributional terminal constraint, and affine/2-norm chance constraints on the state and control, as convex functions of the decision variables. This is leveraged to formulate the chance-constrained path planning problem as a single convex optimization problem. A numerical example demonstrates the effectiveness of the proposed method.

math.OC↗

arXiv2022

SCALER: A Tough Versatile Quadruped Free-Climber Robot

This paper introduces SCALER, a quadrupedal robot that demonstrates climbing on bouldering walls, overhangs, ceilings and trotting on the ground. SCALER is one of the first high-degrees of freedom four-limbed robots that can free-climb under the Earth's gravity and one of the most mechanically efficient quadrupeds on the ground. Where other state-of-the-art climbers specialize in climbing, SCALER promises practical free-climbing with payload \textit{and} ground locomotion, which realizes true versatile mobility. A new climbing gait, SKATE gait, increases the payload by utilizing the SCALER body linkage mechanism. SCALER achieves a maximum normalized locomotion speed of $1.87$ /s, or $0.56$ m/s on the ground and $1.0$ /min, or $0.35$ m/min in bouldering wall climbing. Payload capacity reaches $233$ % of the SCALER weight on the ground and $35$ % on the vertical wall. Our GOAT gripper, a mechanically adaptable underactuated two-finger gripper, successfully grasps convex and non-convex objects and supports SCALER.

cs.RO↗