Time-optimal Velocity Profile Research Articles

A curvature-segmentation-based minimum time algorithm for autonomous vehicle velocity planning

Velocity planning serves as an important issue in motion planning for autonomous vehicles. The presented paper proposes a novel velocity planning method with minimum moving time on the basis of path curvature which is accomplished in three steps. First, the assigned path is divided into some elementary parts based on the path curvature. Second, the velocity planning is transformed into an unconstrained optimization problem by assuming the velocity of vehicle to be a specific cubic polynomial on every elementary part to avoid a sudden acceleration in path switching. Finally, we use a modified projection particle swarm optimization (PPSO) algorithm to obtain the time-optimal velocity profile. The proposed method can generate a smooth time-optimal velocity profile while considering all possible relevant constraints. Three examples are provided on different types of path to demonstrate that the final velocity profile is efficient to avoid the sudden acceleration change. Furthermore, the modified PPSO algorithm in this paper is used to solve the optimization problem with high dimensional variables when its upper bound is known, which can not be achieved by the general PPSO algorithm.

Autonomous Parking Trajectory Planning With Tiny Passages: A Combination of Multistage Hybrid A-Star Algorithm and Numerical Optimal Control

This paper introduces an autonomous parking trajectory planning method in an unstructured environment with narrow passages. The proposed hierarchical trajectory planner consists of a graph search layer and a numerical optimal control layer. The contribution mainly lies in the graph search layer, wherein a multistage hybrid A* algorithm is proposed to handle narrow passages formed by obstacles in the cluttered environment. In the multistage hybrid A* algorithm, a 2-dim A* search is conducted to find a global route that connects the starting and goal points. Along the derived global route, subtle segments that traverse narrow passages are extracted. Thereafter, the hybrid A* algorithm is used to plan kinematically feasible subpaths that connect the boundary points of each subtle segment. The hybrid A* algorithm is also used to find linking paths that connect adjacent subpaths. Combining all the subpaths and linking paths in a sequence yields a coarse path, which is converted into a coarse trajectory by attaching a time-optimal velocity profile to it. The coarse trajectory is fed into the numerical optimization layer as the initial guess. Simulation results indicate that the hierarchical trajectory planner runs much faster than prevalent ones in dealing with unstructured environments with narrow passages.

Integrating time-optimal motion profiles with position control for a high-speed permanent magnet linear synchronous motor planar motion stage

This note addresses the high-speed, high-precision point-to-point motion control of an air-bearing planar stage. The custom-designed stage uses four air-bearings to levitate the stage for the high-speed frictionless operation. Because of the floating nature, the controller for the system needs to overcome the nonlinear free-moving dynamics of the stage and achieve the required performance. To fulfill this purpose, we propose a unique integrated control structure that allows both velocity and reference position inputs. With the proposed structure and the weighting design, it is possible to use the H∞ chain scattering description (H∞-CSD) synthesis for the control parameters. The single structure is used for both the point-to-point movement and the high precision positioning. The reference velocity input enables the long-stroke time-optimal velocity profile injection. The controller converges to the popular PDF control when the stage comes close to the target position. The H∞ specifications enable a robust performance against the load uncertainty. The control undergoes no switching and is thus free from the undesirable chattering. The experimental results show that the proposed control achieves an ultrahigh precision control of 20 nm within 200 ms for a 9-kg stage with 20-mm x, y motion ranges.

Dual-optimization trajectory planning based on parametric curves for a robot manipulator

This article presents a dual-optimization trajectory planning algorithm, which consists of the optimal path planning and the optimal motion profile planning for robot manipulators, where the path planning is based on parametric curves. In path planning, a virtual-knot interpolation is proposed for the paths required to pass through all control points, so the common curves, such as Bézier curves and B-splines, can be incorporated into it. Besides, an optimal B-spline is proposed to generate a smoother and shorter path, and this scheme is especially suitable for closed paths. In motion profile planning, a generalized formulation of time-optimal velocity profiles is proposed, which can be implemented to any types of motion profiles with equality and inequality constraints. Also, a multisegment cubic velocity profile is proposed by solving a multiobjective optimization problem. Furthermore, a case study of a dispensing robot is investigated through the proposed dual-optimization algorithm applied to numerical simulations and experimental work.

Sequential Time-Optimal Path-Tracking Algorithm for Robots

This paper focuses on minimum-time path tracking, a subproblem in motion planning of robotic systems. We generate a time-optimal velocity profile for robotic manipulators taking into account kinematic and dynamic constraints. Based on the special structure of the constraints (called peaked constraints), profile generation is formulated as a linear programming (LP) problem. The LP-based control problem is solved by a sequential optimization method. The presented algorithm has reduced computational time compared to a general LP solver.

Time-optimal velocity planning along predefined path for static formations of mobile robots

This paper is concerned with the problem of finding a time-optimal velocity profile along the predefined path for static formations of mobile robots in order to traverse the path in shortest time and to satisfy, for each mobile robot in the formation, velocity, acceleration, tip over and wheel slip prevention constraints. Time-optimal velocity planning is achieved using so called bang-bang control where minimum and maximum accelerations of the formation are alternating. The developed trajectory planning algorithm is demonstrated on the formation of differential drive mobile robots.

Motion planning of autonomous mobile robots by iterative dynamic programming

We propose a new offline motion planning method for autonomous mobile robots. To minimize traveling time, a smooth path and a time-optimal velocity profile should be generated under kinematic and dynamic constraints. In this study, we develop an effective and practical method to generate a good solution with lower computation time. The initial path is obtained from a Voronoi diagram and spline function, and is improved by iteratively changing via-points. We apply a dynamic programming algorithm to change the via-points, and a Hermite interpolation to generate a smooth trajectory. Simulation results are presented to verify the performance of the proposed method.

동적프로그래밍을 이용한 자율이동로봇의 동작계획

We propose a motion planning method for autonomous mobile robots. In order to minimize traveling time, a smooth path and a time optimal velocity profile should be generated under kinematic and dynamic constraints. In this paper, we develop an effective and practical method to generate a good solution with lower computation time. The initial path is obtained from voronoi diagram by Dijkstra's algorithm. Then the path is improved by changing the graph and path simultaneously. We apply the dynamic programming algorithm into the stage of improvement. Simulation results are presented to verify the performance of the proposed method.

A Discrete-Time Modified Sliding Mode Proximate Time-Optimal Servomechanism for Scanning-Probe-Microscope-Based Data Storage

In this paper, we present a discrete-time modified sliding mode proximate time-optimal servomechanism (MSMPTOS) applied to scanning probe microscope (SPM)-based data storage (SDS) systems. Three conditions on the global asymptotic stability are introduced. Time-varying sliding mode with variable convergence rate factor is used to eliminate the overshoot problem and reduce the settling time compared to the conventional sliding mode proximate time-optimal servomechanism (SMPTOS). For long track seek, its trajectory is bounded by a velocity profile that is close to time-optimal velocity profile. Its settling performance is hardly affected by seek distance whereas reducing seek time. We have obtained improved seek performance over SMPTOS for short and long seeks. Its effectiveness is verified with simulation results.

Optimal Velocity Planning of Wheeled Mobile Robots on Specific Paths in Static and Dynamic Environments

AbstractThis paper deals with optimal temporal‐planning of wheeled mobile robots (WMRs) when navigating on predefined spatial paths. A method is proposed to generate a time‐optimal velocity profile for any spatial path in static environments or when mobile obstacles are present. The method generates a feasible trajectory to be tracked by fully exploiting velocity, acceleration and deceleration boundaries of the WMR, and by ensuring the continuity of the velocity and acceleration functions. As an additional benefit for the tracking process the jerk is also bounded. The algorithm is not time consuming, since it mostly uses closed mathematical expressions, nonetheless iteration strategies are presented to solve specific situations. However, such situations are not expected to occur when the spatial paths are planned as smooth curves. The success of the algorithm was tested by experimental and simulation results on the WMR “RAM.” © 2003 Wiley Periodicals, Inc.

Time optimal path planning for a wheeled mobile robot

This paper investigates time optimal path planning under kinematic and dynamic constraints for a 2-DOF wheeled mobile robot (WMR). The dynamic model of a WMR is derived using the Newton–Euler method and the constraints are analyzed. Kinematic constraints are imposed by WMR's nonholonomy and structural limits, while dynamic constraints are due to motor saturation. The path planning is formulated as a two-stage planning. First, path planning under kinematic constraints is transformed into a pure geometric problem. The shortest path composed of circular arcs and straight lines is obtained. Then, a time optimal velocity profile is generated under dynamic constraints. Since constraints of a WMR are fully exploited, the proposed method is simple and effective. Simulation results are demonstrated. © 2000 John Wiley & Sons, Inc.