Yuichi Tazaki

Finite Abstractions of Discrete-Time Linear Systems and Its Application to Optimal Control

Abstract Optimal control and reachability analysis of continuous-state systems often require computational algorithms with high complexity. The use of finite abstractions of continuous-state systems reduces such problems to path-planning problems on directed graphs with a finite number of nodes, which can be computed efficiently. In this research, we propose a method to design an approximately bisimilar finite abstraction of stabilizable discrete-time linear systems, considering the minimization of the complexity of the resultant finite automaton. Moreover, we show that a suboptimal solution to optimal control problems with a known error bound is obtained by simulating the optimal path of an approximately bisimilar finite abstraction.

Modeling and Analysis of Driving Behavior Based on a Probability-Weighted ARX Model

This paper proposes a probability-weighted autoregressive exogenous (PrARX) model wherein the multiple ARX models are composed of the probabilistic weighting functions. This model can represent both the motion-control and decision-making aspects of the driving behavior. As the probabilistic weighting function, a “softmax” function is introduced. Then, the parameter estimation problem for the proposed model is formulated as a single optimization problem. The “soft” partition defined by the PrARX model can represent the decision-making characteristics of the driver with vagueness. This vagueness can be quantified by introducing the “decision entropy.” In addition, it can be easily extended to the online estimation scheme due to its small computational cost. Finally, the proposed model is applied to the modeling of the vehicle-following task, and the usefulness of the model is verified and discussed.

Discrete Abstractions of Nonlinear Systems Based on Error Propagation Analysis

This paper proposes a computational method for the feasibility check and design of discrete abstract models of nonlinear dynamical systems. First, it is shown that a given discrete-time dynamical system can be transformed into a finite automaton by embedding a quantizer into its state equation. Under this setting, a sufficient condition for approximate bisimulation in infinite steps of time between the concrete model and its discrete abstract model is derived. The condition takes the form of a set of linear inequalities and thus can be checked efficiently by a linear programming solver. Finally, the iterative refinement algorithm, which generates a discrete abstract model under a given error specification, is proposed. The algorithm is guaranteed to terminate in finite iterations.

Bisimilar Finite Abstractions of Interconnected Systems

This paper addresses the design of approximately bisimilar finite abstractions of systems that are composed of the interconnection of smaller subsystems. First, it is shown that the ordinary notion of approximate bisimulation does not preserve the interconnection structure of the concrete model. Next, a new definition of approximate bisimulation that is compatible with interconnection is proposed. Based on this definition of approximate bisimulation, the design of interconnection-compatible finite abstractions of linear subsystems is discussed.

Approximately bisimilar discrete abstractions of nonlinear systems using variable-resolution quantizers

This paper presents a method for the design of discrete abstract models of nonlinear continuous-state systems under the framework of approximate bisimulation. First, the notion of quantizer embedding, which transforms a continuous-state system into a finite-state system, is extended to a variable-resolution setting. Next, it is shown that the series of conditions for approximate bisimulation can be converted into a set of linear inequalities, which can be verified by a linear programming solver. From this result, we obtain an algorithm that repeatedly refines a variable-resolution mesh until approximate bisimulation with a prescribed error specification is achieved.

Model predictive driver assistance control for cooperative cruise based on hybrid system driver model

This paper presents a driver assisting system for cooperative cruising of multiple cars. In order to account for personal difference of individual drivers, each drivers vehicle following skill on expressways is identified as a PrARX model, a continuous approximation of hybrid dynamical system. The PrARX model describes the drivers logical decision making as well as continuous maneuvering in a uniform manner. The assisting acceleration is computed in the framework of model predictive control, where the plant model is a platoon of cars coupled with PrARX driver models. For computing assisting outputs in real time, a fast computation method for nonlinear model predictive control based on the continuation technique is employed. The proposed assisting system is tested in numerical simulations and on a driving simulator with a real human driver. The high speed calculation of the Homotopy method is also proved by comparison to the conventional method. Finally, the advantage of global optimization for cooperative safety is confirmed by comparing its control performance with the local optimization for individual safety.

Model predictive assisting control of vehicle following task based on driver model

A personalized driver assisting system that makes use of the drivers behavior model is developed. As a model of driving behavior, the Probability-weighted ARX (PrARX) model, a type of hybrid dynamical system models, is introduced. A PrARX model that describes the drivers vehicle-following skill on expressways is identified using a simple gradient descent algorithm from actual driving data collected on a driving simulator. The obtained PrARX model describes the drivers logical decision making as well as continuous maneuver in a uniform manner. Finally, the optimization of the braking assist is formulated as a mixed-integer linear programming (MILP) problem using the identified driver model, and computed online in the model predictive control framework.

Trajectory planning for automated parking using multi-resolution state roadmap considering non-holonomic constraints

This paper presents a trajectory planning method for automated parking. The proposed method constructs a state roadmap in which each node contains not only position but also orientation information of the vehicle. The roadmap is constructed by dividing the orientation space in multiple resolutions considering the non-holonomic constraints of the vehicle and the collision-avoidance constraints between the vehicle and the boundary of the parking environment. Using the state roadmap, a complex parking trajectory composed of both forward and reverse motions can be computed with small online computation cost. The proposed method is evaluated in both numerical simulations and an experiment using an electric vehicle.

Constraint-Based Prioritized Trajectory Planning for Multibody Systems

This paper presents a trajectory-planning method for multibody systems. Trajectory planning of a multibody system is formulated as a constraint-solving problem on a set of variables expressing the motion of the multibody system over a unite-time interval. Constraints express the dynamics of rigid bodies, kinematic conditions of joints, various range limitations, as well as achievement of tasks, and they can be assigned different priority levels. The prioritized constraint-solving problem is then treated under the framework of lexicographical goal programming, where the local optimality of the problem is characterized in terms of Pareto efficiency condition. Based on this observation, an algorithm that iteratively updates the variables toward a locally optimal solution is derived. The proposed method is evaluated in simulation examples.

Variable-resolution velocity roadmap generation considering safety constraints for mobile robots

This research develops a new roadmap method for autonomous mobile robots based on variable-resolution partitioning of a continuous state space. Unlike conventional roadmaps, which include position information only, the proposed roadmap also includes velocity information. Each node of the proposed roadmap consists of a fixed position and a range of velocity values, where the velocity ranges are determined by variable-resolution partitioning of the velocity space. An ordered pair of nodes is connected by a directed link if any combination of their velocity values is within the acceptable range of the nodes and produces a trajectory satisfying a set of safety constraints. In this manner, a possible trajectory connecting an arbitrary starting node and destination node is obtained by applying a graph search technique on the proposed roadmap. The proposed method is evaluated through simulations.