Sepanta Sekhavat

Motion planning in dynamic environments: obstacles moving along arbitrary trajectories

This paper generalizes the concept of velocity obstacles given by Fiorini et al. (1998) to obstacles moving along arbitrary trajectories. We introduce the nonlinear velocity obstacle, which takes into account the shape, velocity and path curvature of the moving obstacle. The nonlinear v-obstacle allows selecting a single avoidance maneuver (if one exists) that avoids any number of obstacles moving on any known trajectories. For unknown trajectories, the nonlinear v-obstacles can be used to generate local avoidance maneuvers based on the current velocity and path curvature of the moving obstacle. This elevates the planning strategy to a second order method, compared to the first order avoidance using the linear v-obstacle, and zero order avoidance using only position information. Analytic expressions for the nonlinear v-obstacle are derived for general trajectories in the plane. The nonlinear v-obstacles are demonstrated in a complex traffic example.

Towards real-time global motion planning in a dynamic environment using the NLVO concept

This paper focuses on real-time global motion planning in a dynamic environment. Most of the existing approaches suffer from heavy computation and cannot satisfy real-time constraints. In this paper we present a novel approach, based on the Non-Linear Velocity Obstacle Concept, that maps the positions of the obstacles and their known or estimated trajectories directly in the space of the velocities admissible by our robot, taking into account its kinematic and dynamics constraints. The result is a map of all the collision free velocities. We present a few improvements to this approach and introduce the notion of risk to perform local goal-oriented obstacle-avoidance. Combining it with graph-expansion techniques, we propose to extend the system to an incremental global motion planner in a dynamic environment.

Concurrent matching, localization and map building using invariant features

A common way of localization in robotics is using triangulation on a system composed of a sensor and some landmarks (which can be artificial or natural). First, when no identifying marks axe set on the landmarks, their identification by a robust algorithm is a complex problem which may be solved thanks to correspondence graphs. Second, when the localization system has no a priori information about its environment, it has to build its own map in parallel with estimating its position, a problem known as the simultaneous localization and mapping (SLAM). Recent works have proposed to solve this problem based on building a map made of invariant features. This paper describes the algorithms and data structure needed to deal with landmark matching, robot localization and map building in a single efficient process, unifying the previous approaches. Experimental results axe presented using an outdoor robot car equipped with a 2D scanning laser sensor.

Nonholonomic deformation of a potential field for motion planning

One of the approaches to collision-free nonholonomic motion planning is the approximation method. The corresponding planners compute first a holonomic path among obstacles before approximating it by a concatenation of feasible collision-free paths. These methods are one of the rare ones which can lead to exact and complete planners. However, the performance of these planners (in terms of computation time and the complexity of the solution) is highly influenced by the quality of the first geometric path. We suggest a way to estimate this quality and present the first general approach leading to an improvement of the quality of the geometric path. This approach is based on local deformations of a holonomic potential field with respect to the nonholonomic constraints of the system.

Feedback control of a bi-steerable car using flatness application to trajectory tracking

Bi-steerable cars are four wheel drive robots with a double-axle steering capability. We tackle the stabilization problem for this kind of nonholonomic system by exploiting its flatness property. After deriving new relations between the flat output dynamics and the robot controls, an endogenous dynamic feedback is computed in order to linearize the system and stabilize it around a reference trajectory. Simulation and experimental results using a real bi-steerable car demonstrate the robustness of the approach.

Time optimal paths for a mobile robot with one trailer

Optimal paths are in many ways interesting to motion planning. Not only they are obviously the most interesting ones with respect to the optimized criterion, but also they offer a way of studying the topological aspects associated to the controllability of the system. Many works have been carried out successfully on the optimal paths for unicyle and carlike system. This paper aims to extend those results when adding trailers. Characterizing the time optimal paths for a mobile robot with n-trailers is an ambitious task. As a first step, we give an explicit description of the abnormal and singular extremals for a mobile robot with one trailer. This is done with the help of the maximum principle.

Simultaneous localization and mapping using the Geometric Projection Filter and correspondence graph matching

A common way of localization in robotics is using triangulation on a system composed of a sensor and some landmarks (which can be artificial or natural). First, when no identifying marks are set on the landmarks, their identification by a robust algorithm is a complex problem which may be solved using correspondence graphs. Secondly, when the localization system has no a priori information about its environment, it has to build its own map in parallel with estimating its position, a problem known as simultaneous localization and mapping (SLAM). Recent works have proposed to solve this problem based on building a map made of invariant features. This paper describes the algorithms and data structure needed to deal with landmark matching, robot localization and map building in a single efficient process, unifying the previous approaches. Experimental results are presented using an outdoor robot car equipped with a two-dimensional scanning laser sensor.

The Cycab robot: a differentially flat system

The Cycab robot is a new mobile platform already used in several research labs and meant for different applications such as public transportation in airport terminals, self-service cars in pedestrian zones, etc. From a kinematic point of view, the Cycab specificity is the turning of its rear wheels as a linear function of the steering angle of the front wheels. This feature enhances the maneuverability of the Cycab in cluttered environments. However, the associated kinematic model is new and different from the ones commonly treated in the robotics literature (such as the car-like, tractor-trailer, etc). To our knowledge such a system has not yet been studied and especially, there is no existing motion planner for this system. We tackle the study of this new nonholonomic system, by establishing its kinematic model and proving its differential flatness property. From this study we deduce a first motion planner for the system.

Localization space: a framework for localization and planning, for systems using a sensor/landmarks module

One of the common ways of localization in robotics is the triangulation using a system composed of a sensor and some landmarks (which can be artificial or natural). This paper presents a framework, namely the localization space, in order to deal with problems such as the landmark placement and motion planning including the localization constraint. Based on this framework, we present general approaches to the optimal distribution of the landmarks or to the computation of reliable trajectories. The case of a mobile robot equipped with an orientable sensor (such as a pan vision system) is presented to illustrate the formal concepts and to show the practical relevance of the proposed tools.

Motion Planning in Dynamic Environments

Motion planning in dynamic environments is made possible using the concept of velocity obstacles. It maps the colliding velocities of the robot with any moving or static obstacle to the robot’s velocity space. Collision avoidance is achieved by selecting the robot velocity outside the velocity obstacles. This concept was first proposed in [3] for the linear case of obstacles moving on straight line trajectories, and is extended here to obstacles moving along arbitrary trajectories. The non-linear velocity obstacle (NLVO) takes into account the shape, velocity and path curvature of the moving obstacle. It allows to select a single avoidance maneuver (if one exists) that avoids any number of obstacles that move on any known trajectories. The nonlinear v-obstacle can be generated as a time integral of the colliding velocities, or by computing its boundaries using analytic expressions.