J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Paci c J. Math., 145(2):367-393, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the inputs and the trajectories, the inputs are suboptimal and these methods do not lend themselves to incorporating general types of constraints like for example, obstacles in the environment. The first fundamental result in motion planning for car like systems was derived by Reeds and Shepp [10]. Building on the work of Dubins [11] they showed that minimum distance trajectories for a car are composed of straight lines and circular arcs. Laumond et al. 12] proposed an efficient algorithm for planning near minimum distance trajectories for a car moving among obstacles. Their planning ....

....and forces, and constraints due to obstacles) will be described as state and input based inequality constraints. We assume that it is meaningful to minimize an integral cost or performance function. In tasks in which dynamic considerations are not important, it may be useful to minimize distance [10]. A minimum jerk functional has been advocated for modeling reaching by humans [18] for generating smooth robot trajectories [19] When manipulating objects, it is necessary to maintain force closure while minimizing the contact forces. Therefore, there are constraints on the exerted forces and ....

J. A. Reeds and L. A. Shepp, "Optimal paths for a car that goes both forwards and backwards," Pacific Journal of Mathematics, vol. 145, no. 2, pp. 367--393, 1990.

....model is simpler, and the structure and cost of the fastest trajectories can be determined analytically. Most of the work on time optimal control with bounded velocity models has focused on steered vehicles rather than diff drives, originating with papers by Dubins [3] and by Reeds and Shepp [5]. Many of the techniques employed here are an extension of optimal control techniques developed for steered vehicles in [8, 9, 10] 2 Assumptions, definitions, notation The state of the robot is q = x, y, #) where the robot reference point (x, y) is centered between the wheels, and the robot ....

J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathematics, 145(2):367--393, 1990.

....as in Example 1. Because the starting and goal orientation angle di#er considerably, the WMR trajectory is generated as composed of two arcs and a straight line between them. There are few groups of possible robot trajectories, composed of straight line segments and tangential circular lines [19]. Two circles are passing through the starting point with a radius R = L sin(#max ) At the beginning the WMR performs a turn with a maximum steering angle, after that it moves on the trajectory, around the straight line connecting the two tangential points, and finally it turns again on a ....

J. Reeds and L. Shepp, Optimal paths for a car that goes both forwards and backwards, Pacific Journ. of Mathemat. 145 (1990), no. 2, 367--393.

....as in Example 1. Because the starting and goal orientation angle di#er considerably, the WMR trajectory is generated as composed of two arcs and a straight line between them. There are few groups of possible robot trajectories, composed of straight line segments and tangential circular lines [16]. Two circles are passing through the starting point with a radius R = L sin(#max ) At the beginning the WMR performs a turn with a maximum steering angle, after that it moves on the trajectory, around the straight line connecting the two tangential points, and finally it turns again on a ....

J. Reeds and L. Shepp, "Optimal paths for a car that goes both forwards and backwards," Pacific Journal of Mathematics, vol. 145, no. 2, pp. 367--393, 1990.

....moving in formation using de centralized controllers. The research on control and motion planning for mobile robots is both extensive and diverse. In the area of mobile robots, optimal motion plans for a single car like robot have been thoroughly studied, including results of Reeds and Shepp [1], who proved that optimal paths in a free environment consist of straight lines and circular arcs. Other researchers [2] have studied the development of motion plans for mobile robots in the presence of obstacles, and in particular for systems using only local, or sensor based, planning. One ....

....that there is a constant offset, u = 0 0u, in steady state. If we assume that the lead robot is moving in a straight line, then we arrive at the result of Corollary 2. The optimal point to point paths of a nonholonomic car with constraints on the turning radius were shown by Reeds and Shepp [1] to be com posed of straight lines and circular arcs. This is seen to be generally true even for more complicated systems from the numerical results pre sented in [9] Hence, in this section, we only in vestigate motions involving straight lines and cir cular arcs. Castor Castor. ho d . t ....

J. A. Reeds and L. A. Shepp, "Optimal paths for a car that goes both forwards and backwards," Pacific. Journal of Math., vol. 145, no. 2, pp. 367 393, 1990.

....circles hug the obstacle boundaries in the corridor. As expected flom the cost function, there is a tendency for the platforms to travel, roughly speaking, along straight lines in the obstacle flee region. When the platforms turn, the arcs have the same minimal turning radius as predicted by [34] for a single platform. except in very simple examples. Finally, we note that the generation of optimal trajectories for the examples shown here with a mesh of 200 points takes approximately 60 seconds on a Sparc 10 station. 6 Planar manipulation with a twofingered hand x [m] Figure 11: The ....

J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific. J. of Math., 145(2):367 393, 1990.

....how paths avoiding obstacles can be obtained. However, very few results are available for the synthesis of open loop controls. The generation of optimal trajectories for nonholo nomic systems has been addressed in [10] A funda mental result for car like systems was derived by Reeds and Shepp [11]. Building on the work of Dubins [12] they have showed that minimum distance trajectories for a car are composed of circular arcs and straight lines. Using this result, Laumond et al. 13] have proposed an efficient algorithm for planning near minimum distance trajectories for a car moving among ....

....points and motions of the two platforms during a parallel parking maneuver. The object is moved laterally through a 1 meter distance. The arcs in the platform trajectories at the beginning and towards the end of the maneuver turn out to have the same minimal turn ing radius as predicted by [11] for a single platform. In Figure 7.a and 7.b, the path of the reference point and motions of the two platforms is shown for a 90 degree turn without moving the object significantly (see Figure 3) Similarly, an example of the reconfig uring maneuver is shown in Figure 8. The required linear ....

J. A. Reeds and L. A. Shepp, "Optimal paths for a car that goes both forwards and backwards," Pacific. J. of Math., vol. 145, no. 2, pp. 367 393, 1990.

.... by circular arcs of minimum radius [7] These paths have optimal length: this is an evidence in the case of unconstrained or manoeuvrable robots, and has been proved by Dubins for car like robots going only forward [2] and by Reeds and Shepp for car like robots going both forward and backward [12]. Unfortunately, in any case, these paths cannot be followed precisely without stopping at each discontinuity (of the direction in the first case, of the turning radius in the second) to reorient the robot s directing wheels. To avoid these stops, the use of continuous curvature paths has been ....

J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathemat- ics, 145(2):367 393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Paci c J. Math., 145(2):367-393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Paci c J. Math., 145(2):367-393, 1990. 34

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Reeds and L. Shepp, "Optimal paths for a car that goes both forwards and backwards," in Pacific Journal of Mathematics, vol. 145(2), 1990, pp. 367--393.

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Reeds and L. Shepp, "Optimal paths for a car that goes both forwards and backwards," in Pacific Journal of Mathematics, vol. 145(2), pp. 367--393, 1990.

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J.A. Reeds and L.A. Shepp. Optimal path for a car that goes both forwards and backwards. In Pacific Journal of Mathematics, vo.l 145, 1990

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Reeds, J.A. and L.A. Shepp (1990). "Optimal paths for a car that goes both forwards and backwards".

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J.A. Reeds and L.A. Shepp. "Optimal paths for a car that goes both forwards and backwards" . Pacific Journal of Mathematics , 145(2):367--393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific J. Math., 145(2):367--393, 1990.

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Reeds and L. Shepp, "Optimal paths for a car that goes both forwards and backwards," in Pacific Journal of Mathematics, vol. 145(2), 1990, pp. 367--393.

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Reeds and L. Shepp, "Optimal paths for a car that goes both forwards and backwards," in Pacific Journal of Mathematics, vol. 145(2), pp. 367--393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathematics, 145(2):367--393, 1990.

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J.A. Reeds and R.A. Shepp. Optimal paths for a car that goes both forward and backward. Pacific Journal of Mathematics, 145(2), 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathematics, 145(2):367--393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathematics, 145(2):367--393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathematics, 145(2):367--393, 1990.

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J. A. Reeds and L. A. Shepp. Optimal paths for a car that goes both forwards and backwards. Pacic Journal of Mathematics, 145(2), 1990.

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J.A. Reeds and L.A. Shepp, "Optimal paths for a car that goes both forward and backward," Pacific Journal of Mathematics, vol. 2, pp. 367--393, 1990.

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