Behcet Acikmese

We address motion planning for a mobile agent to acquire information from multiple monitored targets using sensors with limited capabilities. To represent sensor limitations, such as range, field of view, and allowed acquisition directions, we introduce a nonnegative metric that quantifies the rate of information acquisition and is positive only when these limitations are satisfied. To enable optimization-based trajectory generation, we impose temporal logic specifications to ensure that the information acquisition metric and its gradient are nonzero over some time interval. This enables the application of continuous-time successive convexification to solve the motion planning problem. We demonstrate the proposed approach in a case study of a quadrotor that must acquire information on multiple targets with sensor range, field of view, and acquisition direction constraints.

A fundamental issue at the core of trajectory optimization on smooth manifolds is handling the implicit manifold constraint within the dynamics. The conventional approach is to enforce the dynamic model as a constraint. However, we show this approach leads to significantly redundant operations, as well as being heavily dependent on the state space representation. Specifically, we propose an intrinsic successive convexification methodology for optimal control on smooth manifolds. This so-called iSCvx is then applied to a representative example involving attitude trajectory optimization for a spacecraft subject to non-convex constraints.

Discrete-Time Lossless Convexification (DT-LCvx) formulates a convex relaxation for a specific class of discrete-time non-convex optimal control problems. It establishes sufficient conditions under which solutions of the relaxed problem satisfy the original non-convex constraints at specified time grid points. Furthermore, it provides an upper bound on the number of time grid points where these sufficient conditions may not hold, and thus the original constraints could be violated. This paper extends DT-LCvx to problems with control pointing constraints. Additionally, it introduces a novel DT-LCvx formulation for mixed-integer optimal control problems in which the control is either inactive or constrained within an annular sector. Such formulation broadens the feasible space for problems with pointing constraints. A numerical example is provided to illustrate its application.

First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning–the hypersphere preconditioner-for a class of quadratic cone programs (QCPs), i.e., conic optimization problems with a quadratic objective function, wherein the objective function is strongly convex and possesses a certain structure. This approach lends itself to factorization-free, customizable, first-order conic optimization for online applications wherein the solver is called repeatedly to solve problems of the same size/structure, but with changing problem data. We demonstrate the efficacy of our approach on numerical convex and nonconvex trajectory optimization examples, using a first-order conic optimizer under the hood.

We consider the problem of simultaneous open-loop trajectory design and feedback gain co-design to develop an algorithm for robustly-constrained trajectory optimization for linear time-varying systems with state-and control-dependent perturbations. This extends our previous work sheridan2022equivalent, 10383510 to handle optimization of feedback gains to minimize the effect of external perturbations. This could have applications in e.g. vehicle design, by allowing trajectory optimization techniques to be fed back into the vehicle design phase, informing guidance, navigation, and control system requirements. We also present a numerical simulation demonstrating the practicality of our methods.

We propose Newton-PIPG, an efficient method for solving quadratic programming (QP) problems arising in optimal control, subject to additional set constraints. Newton-PIPG integrates the Proportional-Integral Projected Gradient (PIPG) method with the Newton method, thereby achieving both global convergence and local quadratic convergence. The PIPG method, an operator-splitting algorithm, seeks a fixed point of the PIPG operator. Under mild assumptions, we demonstrate that this operator is locally smooth, enabling the application of the Newton method to solve the corresponding nonlinear fixed-point equation. Furthermore, we prove that the linear system associated with the Newton method is locally nonsingular under strict complementarity conditions. To enhance efficiency, we design a specialized matrix factorization technique that leverages the typical sparsity of optimal control problems in such systems. Numerical experiments demonstrate that Newton-PIPG achieves high accuracy and reduces computation time, particularly when feasibility is easily guaranteed.

A fundamental issue at the core of trajectory optimization on smooth manifolds is handling the implicit manifold constraint within the dynamics. The conventional approach is to enforce the dynamic model as a constraint. However, we show this approach leads to significantly redundant operations, as well as being heavily dependent on the state space representation. Specifically, we propose an intrinsic successive convexification methodology for optimal control on smooth manifolds. This so-called iSCvx is then applied to a representative example involving attitude trajectory optimization for a spacecraft subject to non-convex constraints.

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.