Zhijiang Shao

A unified motion planning method for parking an autonomous vehicle in the presence of irregularly placed obstacles

This paper proposes a motion planner for autonomous parking. Compared to the prevailing and emerging studies that handle specific or regular parking scenarios only, our method describes various kinds of parking cases in a unified way regardless they are regular parking scenarios (e.g., parallel, perpendicular or echelon parking cases) or not. First, we formulate a time-optimal dynamic optimization problem with vehicle kinematics, collision-avoidance conditions and mechanical constraints strictly described. Thereafter, an interior-point simultaneous approach is introduced to solve that formulated dynamic optimization problem. Simulation results validate that our proposed motion planning method can tackle general parking scenarios. The tested parking scenarios in this paper can be regarded as benchmark cases to evaluate the efficiency of methods that may emerge in the future. Our established dynamic optimization problem is an open and unified framework, where other complicated user-specific constraints/optimization criteria can be handled without additional difficulty, provided that they are expressed through inequalities/polynomial explicitly. This proposed motion planner may be suitable for the next-generation intelligent parking-garage system.

Quasi-weighted least squares estimator for data reconciliation

Data reconciliation is important in chemical industries. Because of random and possibly gross errors in measurements, data reconciliation is needed to minimize the measurement errors. The most common estimator for data reconciliation is the weighted least squares, which is not robust. A robust estimator, quasi-weighted least squares, is proposed for data reconciliation. The properties of the estimator are analyzed, and the influence function is used to show that the estimator is robust. Two estimators, weighted least squares and quasi-weighted least squares, are used in atmospheric tower, ethylene separation and air separation process systems. Comparisons with other approaches are made on the steam metering process. The effectiveness of the robust estimator is demonstrated.

Precise trajectory optimization for articulated wheeled vehicles in cluttered environments

An articulated vehicle trajectory optimizer is proposed.Constraint violations between every two adjacent collocation points are considered.A simple but accurate collision avoidance judgment is utilized.Large-scale constraints are incorporated into the optimization objective.Various optimization objectives can be handled by our trajectory optimizer uniformly. Trajectory planning refers to planning a time-dependent path connecting the initial and final configurations with some special constraints simultaneously considered. It is a critical aspect in autonomously driving an articulated vehicle. In this paper, trajectory planning is formulated as a dynamic optimization problem that contains kinematic differential equations, mechanical/environmental constraints, boundary conditions and an optimization objective. The prevailing numerical methods for solving the formulated dynamic optimization problem commonly disregard the constraint satisfactions between every two adjacent discretized mesh points, thus resulting in failure when the planned motions are actually implemented. As a remedy for this limitation, the concept of minute mesh grid is proposed, which improves the constraint satisfactions between adjacent rough mesh points. On the basis of accurate penalty functions, large-scale constraints are successfully incorporated into the optimization criterion, thus transforming the dynamic optimization problem into a static one with simple bounds on the decision variables. Simulation results verify that our proposed methodology can provide accurate results and can deal with various optimization objectives uniformly.

Parallel calculation methods for molecular weight distribution of batch free radical polymerization

Abstract The molecular weight distribution (MWD) is at the core of establishing key quality indices for free radical polymerization processes. Due to large-scale features of the rigorous model, consisting of a very large number of differential and algebraic equations, dynamic simulation of MWD is always challenging. A sequential variable decoupling method (SVD) has been proposed to calculate the MWD for any reasonably large chain-length number. In the current paper, parallel computing methods were developed to accelerate the MWD simulation. Both coarse-grained and fine-grained parallelism methods have been proposed. A theoretical analysis of the proposed methods was conducted to demonstrate its high efficiency in parallel computing. Both Intel multi-core-processor-based and NVIDIA graphics-processing-unit-based parallel computing platforms were implemented, achieving significant speedups in computation for MWD simulation.

Simultaneous dynamic optimization

Our trajectory planner can tackle different requirements or constraints uniformly.Our proposal is systematically tested on a wide range of simulation cases.A Hamiltonian-based index is utilized to judge the optimality of an obtained solution.Differences between min-time and min-length trajectories are investigated. Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal.

Time-Optimal Maneuver Planning in Automatic Parallel Parking Using a Simultaneous Dynamic Optimization Approach

Autonomous parking has been a widely developed branch of intelligent transportation systems. In autonomous parking, maneuver planning is a crucial procedure that determines how intelligent the entire parking system is. This paper concerns planning time-optimal parallel parking maneuvers in a straightforward, accurate, and purely objective way. A unified dynamic optimization framework is established, which includes the vehicle kinematics, physical restrictions, collision-avoidance constraints, and an optimization objective. Interior-point method (IPM)-based simultaneous dynamic optimization methodology is adopted to solve the formulated dynamic optimization problem numerically. Given that near-feasible solutions have been widely acknowledged to ease optimizing nonlinear programs (NLPs), a critical region-based initialization strategy is proposed to facilitate the offline NLP-solving process, a lookup table-based strategy is proposed to guarantee the on-site planning performance, and a receding-horizon optimization framework is proposed for online maneuver planning. A series of parallel parking cases is tested, and simulation results demonstrate that our proposal is efficient even when the slot length is merely 10.19% larger than the car length. As a unified maneuver planner, our adopted IPM-based simultaneous dynamic optimization method can deal with any user-specified demand provided that it can be explicitly described.

Time-optimal trajectory planning for tractor-trailer vehicles via simultaneous dynamic optimization

Trajectory planning is a critical aspect of autonomous tractor-trailer vehicle design. Trajectory planning algorithms usually compute paths first, trajectories are obtained thereafter. This multi-step feature makes those planners inefficacious to handle time-dependent constraints. In this study, we consider the original trajectory planning mission directly, which is described as an optimal control problem containing the kinematics, mechanical/physical constraints, environmental requirements as well as an optimization criterion. In this formulation, only the fundamental driving principles with no special issues (e.g., backing-up maneuver and jackknife) are considered. For example, the prevailing “small-angle assumption” is not utilized to prevent jackknifing. Instead, we only require that different parts of a tractor-trailer vehicle should not collide, since the emergence of jackknife does not physically violate the kinematics. An interior-point method based simultaneous approach is adopted to solve the formulated optimal control problem. Simulation results verify our proposal is capable of handling scenarios with various user-specified requirements.

Spatio-temporal decomposition

Motion planning methodologies for parallel parking have been well developed in the last decade. In contrast to the prevailing and emerging parking motion planners, this work provides a precise and objective description of the parking scenario and vehicle kinematics/dynamics. This is achieved by formulating a unified optimal control problem that is free of subjective knowledge (e.g., human experiences). The concerned optimal control problem, when parameterized into a large-scale nonlinear programming (NLP) problem, is extremely difficult to solve. This bottleneck has hindered many research efforts previously. Although the feasible regions of NLP problems are clearly defined, the majority of NLP-solving processes still require high-quality initial guesses, which accelerate the convergence process. In this work, we propose a spatio-temporal decomposition based initialization strategy to generate reliable initial guesses, so as to facilitate the NLP-solving process. In contrast to the typical facilitation strategies in robotic motion/path planning, our spatio-temporal decomposition strategy considers only objective kowledge, further breaking the limitation of subjective knowledge and making full use of a vehicles maneuver potential. A series of comparative simulations verifies that the proposed initialization strategy is advantageous over its prevailing competitors, and that the proposed motion planner is promising for on-line planning missions. Theoretical analysis that supports our initialization strategy is given as well.

Heterogeneous parallel method for mixed integer nonlinear programming

Abstract In a heterogeneous parallel structure, two types of algorithms, Quesada Grossmanns (QG) algorithm and Tabu search (TS), are used to solve mixed integer nonlinear programming (MINLP) simultaneously. Communication is well designed between two threads running the two algorithms individually by exchanging three kinds of information during iterations. First, the best feasible solution in TS can become a valid upper bound for QG. Second, new linearization which can further tighten the lower bound of QG can be generated at the node provided by the TS. Third, additional integer variables can be fixed in QG, thus reducing the search space of TS. Numerical results show that good performance can be achieved by using the proposed method. Further analysis reveals that the heterogeneous method has the potential for superlinear speedup, which may surpass that of the traditional homogeneous parallel method for solving MINLPs.

Module-oriented automatic differentiation in chemical process systems optimization

It is common that external procedures are incorporated into an equation-oriented model when modeling complex chemical process systems. The so-obtained models are called composite models in this paper. Unlike pure equation-oriented models, composite models include hidden variables that cannot be observed externally by the user. In addition, the ratio of the computing time consumed for Jacobian evaluation to the computing time consumed for optimization in composite modeling framework is higher than that required in equation-oriented modeling framework. However, traditional algorithms are not able to fully exploit the structure of composite model so as to effectively improve the efficiency of optimization. In this paper, a module-oriented automatic differentiation (MAD) approach is presented based on traditional automatic differentiation algorithms. This approach can well exploit the sparsity of the model by partitioning it into a series of sequential modules and choosing the best differentiation algorithm for each module accordingly. Moreover, external Jacobian evaluation codes for specific modules can be easily incorporated into this approach. Numerical results demonstrate its advantage of the procedure in optimization.