Chuangchuang Sun

Path Planning of Spatial Rigid Motion with Constrained Attitude

This paper presents a general quadratic optimization methodology for autonomous path planning of spatial rigid motion with constrained attitude. The motion to be planned has six degrees of freedom and is assumed under constant velocity in the body frame. The objective is to determine the motion orientation (or attitude), handled as control variables, along the planned paths. A procedure is discussed to transform the rotational constraints and attitude constraints as quadratic functions in terms of unit quaternions, and the path-planning problem is reformulated as a general, quadratically constrained, quadratic programming problem. A semidefinite relaxation method is then applied to obtain a bound on the global optimal value of the nonconvex, quadratically constrained, quadratic programming problem. Subsequently, an iterative rank minimization approach is proposed to find the optimal solution. Application examples of aircraft path-planning problems are presented using the proposed method and compared with ...

Spacecraft Attitude Control under Constrained Zones via Quadratically Constrained Quadratic Programming

This paper examines an optimal spacecraft attitude control problem in the presence of complicated attitude forbidden zones. The objective is to design an optimal reorientation trajectory for a rigid body spacecraft under constraints, which is originally formulated as a nonlinear programming problem. The attitude forbidden zones are considered to prevent the light-sensitive instruments operated on-board from exposure to bright light while the mandatory zone to keep the communication instrument in certain zones to transmit and receive signals. When unit quaternions are used to represent the attitude of spacecraft, the dynamics and constraints are formulated as quadratic functions. By discretizing the reorientation trajectory into discrete nodes, the optimal attitude control problem can be formulated as general quadratically constrained quadratic programming (QCQP). Due to nonconvexity of general QCQP problems, the traditional semide nite relaxation method can only obtain a bound on the optimal solution. In this paper, we proposed an iterative rank minimization approach to gradually reduce the gap between the bound and the optimal solution and will nally converges to the optima. Simulation results are presented to demonstrate the feasibility of proposed algorithm.

A Flexible Concept for Designing Multiaxis Force/Torque Sensors Using Force Closure Theorem

Multiaxis force/torque sensors have many applications in the areas of robotics and automation. A building blocks concept to design multiaxis force/torque sensors is introduced to provide a flexible and low-cost solution to measure multidimensional force/torque signals using a modularized assembly of several off-the-shelf 1-D force sensors. Based on the force closure theorem, we first identify the relationship between the required number of the 1-D force sensors and the dimensions of the measured force/torque signal. Furthermore, we formulate alternatives of the design solution for a multiaxis force/torque sensor, including the location and direction of each 1-D sensor. A virtual prototype of a six-axis force/torque is developed using this concept. Matrix-based force measuring models are derived to compute the six-axis force/torque signals from the output signals of seven 1-D force sensors. The matrix-based force measuring equations are validated using automatic dynamic analysis of mechanical systems. The output signals of the six-axis force/torque signal is consistent with the reference signals measured by an ATI Nano-17 force/torque sensor. One major advantage of this design concept is its flexibility; we can easily adapt the mechanical structure to design multidimensional force/torque sensors ranging from two degrees of freedom (2-DOFs) to 6-DOFs.

An iterative approach to Rank Minimization Problems

This paper investigates an iterative approach to solve the Rank Minimization Problems (RMPs) constrained in a convex set. The matrix rank function is discontinuous and nonconvex and the general RMP is classified as NP-hard. A continuous function is firstly introduced to approximately represent the matrix rank function with prescribed accuracy by selecting appropriate parameters. The RMPs are then converted to rank constrained optimization problems. An Iterative Rank Minimization (IRM) method is proposed to gradually approach the constrained rank. Convergence proof of the IRM method using the duality theory and Karush-Kuhn-Tucker conditions is provided. Two representative applications of RMP, matrix completion and output feedback stabilization problems, are presented to verify the feasibility and improved performance of the proposed IRM method.

Solving Polynomial Optimal Control Problems via Iterative Convex Optimization

The polynomial optimal control problems (POCPs) have many applications where the objective, dynamics, and constraints are represented by polynomial functions. Through discretization, a POCP can be transformed into a polynomial programming problem. Very few of such problems are convex and thus they are generally classi ed as NP-hard. In this paper, we rst introduce new variables to transform the polynomial objective and/or constraints into quadratic functions to obtain an equivalent formulation of Quadratically Constrained Quadratic Programming (QCQP) problem. Further transformation to matrix linear programming problem with rank-one constraint on the unknown matrix. A successive convex optimization approach, named Iterative Rank Minimization (IRM), is proposed to gradually satisfy the rank constraint. Rigorous proof is provided to verify that IRM can guarantee converging to an optimum of the original problem. The optimal launch ascent problem is solved by the proposed method to verify the e ectiveness and improved performance of the proposed algorithm compared to the results in the literature.

Weighted Network Design with Cardinality Constraints via Alternating Direction Method of Multipliers

This paper examines simultaneous design of the network topology and the corresponding edge weights in the presence of a cardinality constraint on the edge set. Network properties of interest for this design problem lead to optimization formulations with convex objectives, convex constraint sets, and cardinality constraints. This class of problems is referred to as the cardinality-constrained optimization problem (CCOP); the cardinality constraint generally makes CCOPs NP-hard. In this paper, a customized alternating direction method of multipliers (ADMM) algorithm aiming to improve the scalability of the solution strategy for large-scale CCOPs is proposed. This algorithm utilizes the special structure of the problem formulation to obtain closed-form solutions during each iterative step of the corresponding ADMM updates. We also provide a convergence proof of the proposed customized ADMM to a stationary point under certain conditions. Simulation results illustrate that the customized ADMM algorithm has a significant computational advantage over existing methods, particularly for large-scale network design problems.

A decomposition method for nonconvex quadratically constrained quadratic programs

This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using a decomposition method. It is well known that a QCQP can be transformed into a rank-one constrained optimization problem. Finding a rank-one matrix is computationally complicated, especially for large scale QCQPs. A decomposition method is applied to decompose the single rank-one constraint on original unknown matrix into multiple rank-one constraints on small scale submatrices. An iterative rank minimization (IRM) algorithm is then proposed to gradually approach all of the rank-one constraints. To satisfy each rank-one constraint in the decomposed formulation, linear matrix inequalities (LMIs) are introduced in IRM with local convergence analysis. The decomposition method reduces the overall computational cost by decreasing size of LMIs, especially when the problem is sparse. Simulation examples with comparative results obtained from an alternative method are presented to demonstrate advantages of the proposed method.

Rank-constrained optimization and its applications

Abstract This paper investigates an iterative approach to solve the general rank-constrained optimization problems (RCOPs) defined to optimize a convex objective function subject to a set of convex constraints and rank constraints on unknown rectangular matrices. In addition, rank minimization problems (RMPs) are introduced and equivalently transformed into RCOPs by introducing a quadratic matrix equality constraint. The rank function is discontinuous and nonconvex, thus the general RCOPs are classified as NP-hard in most of the cases. An iterative rank minimization (IRM) method, with convex formulation at each iteration, is proposed to gradually approach the constrained rank. The proposed IRM method aims at solving RCOPs with rank inequalities constrained by upper or lower bounds, as well as rank equality constraints. Proof of the convergence to a local minimizer with at least a sublinear convergence rate is provided. Four representative applications of RCOPs and RMPs, including system identification, output feedback stabilization, and structured H 2 controller design problems, are presented with comparative simulation results to verify the feasibility and improved performance of the proposed IRM method.

Distributed estimation for spatial rigid motion based on dual quaternions

This paper proposes a distributed optimization algorithm for estimation of spatial rigid motion using multiple image sensors in a connected network. The objective is to increase the estimation precision of translational and rotational motion based on dual quaternion models and cooperation between connected sensors. The distributed Newton optimization method is applied to decompose the filtering task into a series of suboptimal problems and then solve them individually to achieve the global optimality. Our approach assumes that each sensor can communicate with its neighboring sensors to update the individual estimates. Simulation examples are demonstrated to compare the proposed algorithm with other methods in terms of estimation accuracy and converging rate.