Reactive Path Deformation for Nonholonomic Mobile Robots

Lamiraux, Florent; Bonnafous, David; Lefebvre, Olivier

doi:10.1109/tro.2004.829459

Cited by 147 publications

(91 citation statements)

References 29 publications

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“…Our method also relates to the trajectory optimization literature in robotics [12], [13], [14], [15], though these methods typically focus on improving a pre-supplied (feasible) trajectory via gradient or higher-order methods. Although in this paper we focus on cases where the initial "plan" supplied to the cubic spline optimization problem is very simple and possibly infeasible, there is nothing that prevents the method from being used to optimize a feasible trajectory generated by a planner, as in the approaches above: in this setting the algorithm could also function as a trajectory optimization approach, specifically using a cubic spline parametrization of the trajectory, and using general convex optimization techniques rather than gradient methods alone.…”

Section: Discussion and Related Workmentioning

confidence: 99%

Task-space trajectories via cubic spline optimization

Kolter

2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-We consider the task of planning smooth trajectories for robot motion. In this paper we make two contributions. First we present a method for cubic spline optimization; this technique lets us simultaneously plan optimal task-space trajectories and fit cubic splines to the trajectories, while obeying many of the same constraints imposed by a typical motion planning algorithm. The method uses convex optimization techniques, and is therefore very fast and suitable for real-time re-planning and control. Second, we apply this approach to the tasks of planning foot and body trajectory for a quadruped robot, the "LittleDog," and show that the proposed approach improves over previous work on this robot. I. INTRODUCTIONIn this paper we consider the task of planning smooth trajectories for robot motion. This is one of the fundamental tasks of robotics, and has received a great deal of attention over the past several decades. One strategy that has proven particularly effective for this task is the use of smooth, parametrized splines to describe trajectories, either in jointspace or task-space. Cubic splines in particular are ubiquitous in robotic applications [1], as they provide a simple means of generating smooth (twice differentiable) trajectories for robot motion.Cubic splines for robot trajectories are typically employed as follows. First, one uses a high-level planning algorithm to generate a series of kinematically feasibly waypoints that the robot should pass through on its way to the goal. Next, one fits the parameters of a cubic spline that passes through all these points; the smoothness of the resulting cubic spline leads to a smoother motion of the robot than would be obtained, for example, by a linear spline that just interpolated between the waypoints. We refer to this as the "two-phase" approach, since the planning and spline fitting are done in separate phases.However, despite their advantages, cubic splines also suffer from a number of drawbacks. The chief problem is that in the typical two-phase application of cubic splines, the high-level waypoint planning is done separate from the cubic spline fitting procedure, which can lead to poor trajectories. To convey this intuition, consider the simple planning task shown in Figure 1 (a): the objective is to move a double pendulum, actuated at both joints, from the start to the goal, while avoiding the obstacle. Figure 1 (b) shows a possible output from a typical planner (for example, a randomized tree planner [2]) and the corresponding cubic spline fit to these waypoints. Due to the stochastic nature of the planner, the waypoints do not lead to a particularly nice final trajectory. Existing trajectory optimization techniques [3] can help mitigate this problem to some degree, but they usually

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Section: Discussion and Related Workmentioning

confidence: 99%

Task-space trajectories via cubic spline optimization

Kolter

2009

2009 IEEE International Conference on Robotics and Automation

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“…As the moving disk approaches the path, the path is increasingly deformed until it snaps [6]. Although several motion deformation methods have been proposed [6], [7], [8], [9], [10], all deform only the geometric path and ignore the time dimension of a dynamic environment. This is not entirely satisfactory.…”

Section: A Background and Motivationmentioning

confidence: 99%

From path to trajectory deformation

Kurniawati

Fraichard

2007

2007 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Path deformation is a technique that was introduced to generate robot motion wherein a path, that has been computed beforehand, is continuously deformed on-line in response to unforeseen obstacles. This paper introduces the first trajectory deformation scheme as an effort to improve path deformation. The main idea is that by incorporating the time dimension and hence information on the obstacles' future behaviour, quite a number of situations where path deformation would fail can be handled. The trajectory deformation scheme presented operates in two steps, ie, a collision avoidance step and a connectivity maintenance step, hence its name 2-Step-Trajectory-Deformer (2-STD). In the collision avoidance step, repulsive forces generated by the obstacles deform the trajectory so that it remains collision-free. The purpose of the connectivity maintenance step is to ensure that the deformed trajectory remains feasible, ie, that it satisfies the robot's kinematic and/or dynamic constraints. Moreover, unlike path deformation wherein spatial deformation only takes place, 2-STD features both spatial and temporal deformation. It has been tested successfully on a planar robot with double integrator dynamics moving in dynamic environments.

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“…For instance, [15] introduced the elastic bands as a combined planning and control methodology to dynamically deform paths while allowing real time obstacle avoidance. The idea of dynamically deform paths evolved and met important progresses [8], [3] and provided extensions to higher planning instances [5]. Other approaches exist that attempt to increase the planner reliability by embedding realistic simulators on the planner, [11].…”

Section: Introductionmentioning

confidence: 99%

Path optimization for rhombic-like vehicles: An approach based on rigid body dynamics

Fonte¹,

Valente²,

Vale³

et al. 2011

2011 15th International Conference on Advanced Robotics (ICAR)

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Abstract-This paper proposes a new path optimization method to improve feasibility and optimality of rough collisionfree paths provided by global planners. Inspired on the dynamics of rigid bodies, this method redefines the elastic bands framework to explicitly handle vehicle geometric constraints and explore the high maneuvering ability of rhombic vehicles. The proposed method was tested as a post optimization technique on global path solutions planned for a large transporter that will operate in the International Thermonuclear Experimental Reactor (ITER). Presented results show the proficiency of this method on handling feasible and reliable paths in cluttered scenarios such as those in ITER.

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Reactive Path Deformation for Nonholonomic Mobile Robots

Cited by 147 publications

References 29 publications

Task-space trajectories via cubic spline optimization

Task-space trajectories via cubic spline optimization

From path to trajectory deformation

Path optimization for rhombic-like vehicles: An approach based on rigid body dynamics

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