Waypoint trajectory planning in the presence of obstacles with a tunnel-MILP approach

Afonso, Rubens Junqueira Magalhães; Galvão, Roberto Kawakami Harrop; Kienitz, Karl Heinz

doi:10.23919/ecc.2013.6669574

Cited by 8 publications

(13 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our approach we utilize MILP optimization, which is also used in other MILP-based methods such as [3,19,46,53]. However, there are significant differences between those methods and our approach.…”

Section: Related Workmentioning

confidence: 99%

“…One can also find several approaches relying on formulation of a MILP (mixed-integer linear programming) problem for model-predictive control or planning, utilizing discrete time problem formulations with explicit discretization of controls such as [3,19,46,53]. Another interesting approach shown in [49] depends upon consideration of obstacle avoidance problem using optimal control framework.…”

Section: Related Workmentioning

confidence: 99%

“…It is also worth emphasizing that the algorithms from [3,19,46,53] plan piecewise-constant open-loop control signals, while our method generates a sequence of feedback control policies. The policies are ready to execute and they generate a continuously varying feedback control signal (everywhere except a finite sequence of switching points between the waypoints).…”

Section: Related Workmentioning

confidence: 99%

“…Since one can show thatM i = 0, it suffices to find a solution ofN i = 0, which can be obtained by substitution ν i = y i+1 2μ i and explicit solution of resultant cubic polynomial, yielding two conjugate complex roots and one real rootỹ i+1 given by (19). Existence of a single real root means thatỹ i+1 is exactly the point at which curvature along considered specific integral curve (10) with p i = 1 attains its extremum κ i (ỹ i+1 , 1) .…”

Section: Property 2 Under Nominal Conditions and Formentioning

confidence: 99%

See 3 more Smart Citations

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Gawron

Michałek

2017

J Intell Robot Syst

View full text Add to dashboard Cite

Integrated motion planning and control for the purposes of maneuvering mobile robots under state-and input constraints is a problem of vital practical importance in applications of mobile robots such as autonomous transportation. Those constraints arise naturally in practice due to specifics of robot mechanical construction and the presence of obstacles in motion environment. In contrast to approaches focusing on feedback control design under the assumption of given reference motion or motion planning with neglection of subsequent feedback motion execution, we adopt a controller-driven motion planning paradigm, which has recently gained attention of many researchers. It postulates design of motion planning algorithms dedicated to specific feedback control policies, which compute a sequence of feedback control subtasks instead of classically planned open-loop controls or parametric paths. In this spirit, we propose a motion planning algorithm driven by the VFO (Vector Field Orientation) control law for the waypointfollowing task. Presented analysis of the VFO control law reveals its beneficial properties, which are subsequently utilized to solve a generally nonlinear and non-convex optimal motion planning problem by formulating it as a mixed-integer linear program (MILP). The solution proposed in this paper yields a waypoint sequence, which is designed for execution by application of the VFO control law to drive a robot to a prescribed final configuration under an input constraint imposed by bounded curvature of robot motion and state constraints resulting from a convex decomposition of task space. Satisfaction of these constraints is guaranteed analytically and exactly, i.e., without utilization of numerical approximations. Moreover, for a given discrete set of possible waypoint orientations, the proposed algorithm computes plans optimal w.r.t. given cost functional, which can be any convex linear combination of quantities such as robot path length, curvature of robot motion, distance to imposed state constraints, etc. Furthermore, the planning algorithm exploits the possibility of both forward or backward movement of the robot to allow maneuvering in demanding environments. Generated waypoint sequences are a compact representation of a motion plan, which can be immediately executed with the VFO controller without any additional postprocessing. Validity of the proposed approach has 266 J Intell Robot Syst (2018) 89:265-297 been confirmed by simulation studies and experimental motion execution with a laboratory-scale mobile robot.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Property 2 Under Nominal Conditions and Formentioning

confidence: 99%

See 2 more Smart Citations

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Gawron

Michałek

2017

J Intell Robot Syst

View full text Add to dashboard Cite

show abstract

“…They are deterministic by construction and excel in low-dimensional problem spaces. Their convergence rate may be affected by topology of the environment, but not as much as in the case of sampling-based planners.Some planners using genetic algorithms [3], mathematical programming [12] or other not mentioned before forms of global optimization can be found. The vast majority of motion planners is designed to generate a plan in the form of control signals (e.g.…”

mentioning

confidence: 99%

Planning the Waypoint-Following Task for a Unicycle-Like Robot in Cluttered Environments

Gawron¹,

Michałek²

2015

JAMRIS

View full text Add to dashboard Cite

Abstract:The Introduc onMotion planning for systems with nonholonomic constraints is a topic recently explored by many researchers all around the world. Signi icance of this topic stems from the fact that many wheeled mobile robots and the vast majority of road vehicles are subject to nonholonomic constraints. Ef icient and theoretically sound motion planning in the cluttered environment is paramount to effective automation of wheeled vehicles. While many of the existing motion planners achieve this goal to some extent, they all come with some limitations, which are outlined in the short survey of motion planners presented below. A complete survey of motion planning algorithms can be found in [4,15,17].Availability of powerful computing units has stimulated the development of sampling-based motion planners. Among them, the most successful are Rapidly Exploring Random Trees [13,16] and their variations referred to generally as Rapidly Exploring Dense Trees (see [17]). Those algorithms are applicable to a wide range of systems and perform well in high-dimensional con iguration spaces with no eficient collision checking procedures available. This versatility is achieved by means of probabilistic sampling in the problem space and particular method of extending the tree of possible solutions. Unfortunately, those algorithms are non-deterministic, i.e. two runs with equal boundary conditions may not result in the same solution. Moreover, they are not strictly complete, but rather asymptotically complete, which means that there is no guarantee of inding a solution in inite time. Their Voronoi bias property leads to convergence problems in environments containing narrow passages and in the neighborhood of boundary conditions. Many of those problems can be ixed systematically (see [10]) or heuristically (see [1]) by making speci ic trade-offs. Most of these algorithms rely on numerical simulation of system's evolution for exploring the problem space and make use of no other system-speci ic information.The other major class of motion planners is formed by grid-based algorithms, which model the problem space as a multidimensional lattice. That lattice is searched systematically for a feasible path with algorithms such as Dijkstra, Value Iteration, A* or their variations [2,5]. Effectiveness of the planner depends on choice of the search space and specialization of the search algorithm. Many search spaces were proposed, some of them are: control spaces, con iguration space grids with dynamic neighborhoods [8], state lattices constructed with motion primitives [25] and simplicial decompositions searched continuously [27]. Specialization of search algorithms is achieved mainly by rede inition of movement costs in the grid and simple customization of heuristic functions (see [14]). Some variations of grid-based planners include planners searching in the preprocessed decompositions of the problem space such as hierarchical grids, visibility graphs, etc. Grid-based planners are usually resolution complete, i.e. they will always...

show abstract

A Set-Based Trajectory Planning Algorithm for a Network Controlled Skid-Steered Tracked Mobile Robot Subject to Skid and Slip Phenomena

Scordamaglia¹,

Nardi²

2020

J Intell Robot Syst

View full text Add to dashboard Cite

Waypoint trajectory planning in the presence of obstacles with a tunnel-MILP approach

Cited by 8 publications

References 23 publications

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Planning the Waypoint-Following Task for a Unicycle-Like Robot in Cluttered Environments

A Set-Based Trajectory Planning Algorithm for a Network Controlled Skid-Steered Tracked Mobile Robot Subject to Skid and Slip Phenomena

Contact Info

Product

Resources

About