K.G.Shin and N.D.McKay. Minimum time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....energy along the path. The energy model used depends on the robot design and its application; e.g. legged robots could minimize energy consumed by the motors in the legs when operated. This problem is similar to the time optimality problem, which has, perhaps, been analyzed in greater depth [2] 8][7]. Finding energy optimal paths is crucial for many applications such as space exploration, unmanned reconnaissance vehicles where the success of the task depends heavily on conserving available energy. Researchers at Battelle have developed a novel hybrid design (wheeled and legged) called the ....

K.G.Shin and N.D.McKay. Minimum time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 1985.

....TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 20, NO. 6, NOVEMBER DECEMBER 1990 1383 Satisficing Feedback Strategies for Navigation of Autonomous Mobile Robots Local DAI FENG, MEMBER, IEEE, AND BRUCE H. KROGH, MEMBER, IEEE Abstract A general approach to the local navigation problem for autonomous mobile robots (AMRs) and its application to omnidirectional and ....

....complete information about the environment is known a priori. The most notable works in this area have been reported by Lozano Perez [1] 2] Reif [3] Schwartz [4] 5] and O Dunlaing et al. [6] The objective is to move a finite size object (a robot) from a Manuscript received February xx, 1989; revised October 16, 1989. This work was supported in part by the National Science Foundation under Grants ECS 8404607 and DMC 8451493, and in part by the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA. The authors are with Department of Electrical and Computer Engi neering and ....

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K.G. Shin and N. D. McKay, "Minimum-time control of robotics manipulators with geometric path constrains," IEEE Trans. Automat. Contr., vol. AC-30, no. 6, pp. 531 541, June 1985.

....planning in the form we present was first introduced by Bobrow [6] Bobrow s work uses the idea of the admissible path velocities and the admissible regions in phase plane. The admissible regions are calculated from the input torque bounds. This approach was further developed by Shin and McKay [7]. They show that the admissible regions are not necessary simply connected. The application of this method in the practice was done by Dahl and Nielsen[8, 9] They use a feedback scheme for path following scheme with on line trajectory scaling to solve the problem of saturation of the control ....

....to calculate feasible trajectories from a given path with simultaneous utilization of the maximal capabilities of the manipulator. There are different approaches to the calculation of admissible values of s and s based on input constraints. Most of the authors deal with the minimum time problems [6, 7, 8] and consider only the constraints on the input torques. Unfortunately, this is not sufficient in many cases. Actually, the actuators have beside the torque limits also the velocity limits which are as important as the torque limits. On the other hand, the task may require certain velocity ....

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K. G. Shin and N. D. McKay. Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints. IEEE Trans. on Automatic Control, AC30 (6):531 -- 541, 1985.

....control along a specified path is equivalent to the time optimal control of a double integrator system. The optimal solution will therefore be bang bang . In other words, each input is always at its upper or lower limit, and it instantaneously switches between the limits finitely many times [7, 30]. Based on the definition of a velocity limit curve in the two dimensional state space for the specified path, it is possible to compute the switching points [7, 31] There is extensive literature on this subject including algorithms for contact tasks such as contour following [32] and for the ....

K. G. Shin and N. D. McKay, "Minimum-time control of robotic manipulators with geometric constraints," IEEE Transactions on Automatic Control, vol. AC-30, no. 6, pp. 531-541, 1985.

....find a so Issues in Nonprehensile Manipulation 0.3 0.3 0.3[m] Motor Encoder Gear Motor Encoder Gear Encoder Figure 8: The MEL underactuated manipulator. lution when one exists. The planner is resolutioncomplete. Once a path is found, we can apply the algorithms proposed by Shin and McKay [32] or Bobrow et al. 5] to find the time optimal time scaling of each motion segment of the path. The concatenation of these trajectories yields the time optimal trajectory following the path returned by the planner. We implemented planner results on the Mechanical Engineering Laboratory ....

K. G. Shin and N. D. McKay. Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 30(6):531--541, June 1985.

....to incorporate constraints on the joint accelerations. To obtain an s#t# which is monotonically increasing, we require that s # 0, with s =0only at single points. The reader may note that solving Problem 1 is, in principle, equivalent to solving the fixed path minimum time trajectory problem [12, 10]. Solutions to the latter usually consider actuator force torque limits and the full manipulator dynamics, but do not work at singularities. Essentially, the DAO algorithm solves a simplified (i.e. unit dynamics) version of the fixed path minimum time problem, but does so robustly at ....

K. G. Shin and N. D. McKay, "Minimum-time Control of Robotic Manipulators with Geometric Path Constraints." IEEE Transactions on Automatic Control, June 1985, pp. 531-541 (Vol. AC-30, No. 6).

....shown [4, 5, 6] and some authors have modified Jacobian based approaches to this end [7, 8] What the above techniques do not do is generate trajectories with tight bounds on joint acceleration. Indeed, this turns the problem into a variation of the time optimal path following planning problem [9, 10]. We believe that the algorithm described here is the first to produce near minimum time trajectories, given bounds on the joint velocities and accelerations, for any kinematic solution containing ordinary and linear self motion singularities. It is an improvement on an earlier algorithm [11] ....

K. G. Shin and N. D. McKay, "Minimum-time control of robotic manipulators with geometric path constraints," IEEE Transactions on Automatic Control, vol. AC-30, pp. 531--541, June 1985.

....nonlinear controllability, ane connections I. Introduction The problem of nding the time optimal trajectory for a fully actuated robot manipulator along a speci ed path is a classical one in robotics. This problem has been solved by algorithms proposed by Bobrow et al. 1] and Shin and McKay [2], and later enhancements due to Pfei er and Johanni [3] Slotine and Yang [4] and Shiller and Lu [5] These algorithms nd the minimum time time scaling of the path which respects the actuator constraints. With the time scaling algorithms in hand, the problem of nding a fast collision free ....

K. G. Shin and N. D. McKay, \Minimum-time control of robotic manipulators with geometric path constraints," IEEE Transactions on Automatic Control, vol. 30, no. 6, pp. 531-541, 1985.

....equation (4a d) 5) Remark 2.2. Linear parameterization of robots. Note that the parameterization of a robot can be chosen, cf. 1,4,14] such that the dynamic and kinematic equation depend linearly on the parameter vectors p D ; p K . The objective of optimal trajectory planning is to determine [6,7,18,28,30,39,43] a control function u = u(t) t t 0 , such that the cost functional J u( t f Z t 0 L t; p J ; q(t) q(t) u(t) dt t f ; p J ; q(t f ) q(t f ) 6) is minimized, where the terminal time t f may be given explicitly or implicitly, as e.g. in minimum time ....

Shin, K.G.; McKay, N.D.: Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints. IEEE Trans. on Automatic Control, Vol. AC-30, pp. 531-541 (1985)

....implementation. q, q Path Governor Desired Path Primal Controller T s Y (s) d Y ( d Figure 1: Path tracking with on line path parameterization In some joint space robot motion planning schemes, the original limits are translated into constraints on the only reference trajectory [1, 2, 5]. For example, torque saturations are converted in constraints on the desired velocity and acceleration. However, this approach entails in assuming perfect tracking, and consequently part of the robot control system dynamics is neglected. Although this approach leads to computationally efficient ....

K. Shin and N.D. McKay, "Minimum-time control of robotic manipulators with geometric path constraints," IEEE Trans. Robotics Automat., Vol. 30, n. 6, pp. 531-- 541, 1985.

....the singularity (as indicated by the leftmost dotted line in Figure 2.C) Placing tight limits on acceleration therefore necessitates the use of global trajectory planning. Our algorithm does this using techniques similar to those used for general time optimal path following (Bobrow et al. 1985; Shin McKay, 1985; Slotine Yang, 1989) with velocity and acceleration constraints used instead of dynamics based torque constraints. The resulting algorithm produces near minimum time trajectories, in the presence of both ordinary singularities and those involving linear self motions (Section 3.1) It is an ....

....to control the path timing. This is known as coordinate pivoting, and is described in Section 4. Whichever coordinate is used to control the path timing, s or otherwise, is called the driving coordinate, and is denoted by x. In standard time optimal path following procedures (Bobrow et al. 1985; Shin McKay, 1985), the timing s(t) is actually produced implicitly by computing s as a function of s. The same thing is done here, using the driving coordinate x (whose identity will vary along the path) in place of s. The algorithm comprises two main steps: 1. CreateKnots: Knot points s i are introduced along ....

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Shin, Kang G., & McKay, Neil D. 1985. Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints. IEEE Transactions on Automatic Control, AC30 (6), 531--541.

....class of underactuated mechanical systems. 1 Introduction The problem of finding the time optimal trajectory for a fully actuated robot manipulator along a specified path is a classical one in robotics. This problem has been solved by algorithms proposed by Bobrow et al. 1] and Shin and McKay [2], and later enhancements due to Pfeiffer and Johanni [3] Slotine and Yang [4] and Shiller and Lu [5] These algorithms find the minimum time time scaling of the path which respects the actuator constraints. With the time scaling algorithms in hand, the problem of finding a fast collision free ....

K. G. Shin and N. D. McKay, "Minimum-time control of robotic manipulators with geometric path constraints," IEEE Transactions on Automatic Control, vol. 30, no. 6, pp. 531--541, 1985.

....the robot need only be brought to zero at switches between the two velocity vector fields, so the planner minimizes the number of switches. The path returned by the planner can then be time scaled according to the actuator limits to find the time optimal trajectory along the path (Shin and McKay [34]; Bobrow et al. 10] Pfeiffer and Johanni [29] Slotine and Yang [35] Shiller and Lu [33] This approach decouples the problem of collision free trajectory planning into the computationally simpler problems of path planning and time scaling. ffl Fast trajectories. Although local ....

....place bounds on s for a given state (s; s) The problem is to find the fastest trajectory in the (s; s) phase plane from (0; 0) to (1; 0) satisfying the torque constraints. The minimum time time scaling problem has been solved by algorithms proposed by Bobrow et al. 10] Shin and McKay [34], Pfeiffer and Johanni [29] Slotine and Yang [35] and Shiller and Lu [33] The idea is illustrated in Figure 3. At a state (s; s) the set of possible path accelerations [ s min ; s max ] defines a cone of possible motion directions in the (s; s) phase plane. The minimumtime trajectory is ....

K. G. Shin and N. D. McKay. Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 30(6):531--541, June 1985.

....trajectory is also underconstrained. We are thus interested in an optimal trajectory and an optimal load sharing scheme. Previous work in this direction has focused on minimum time trajectories for a single unconstrained robot arm. Minimum time control for a single robot arm has been studied in [1, 2]. In these early works, the optimization problem is simplified by the fact that a prespecified path confines the motion of the system to only one degree of freedom expressed by the path parameter. More recently, Shiller and Dubowsky developed a method for computing the time optimal motions of ....

K. G. Shin and N. D. McKay, "Minimum-time control of robotic manipulators with geometric constraints," IEEE Trans. Automatic Control, vol. AC-30, no. 6, 1985.

....to follow that path. The latter stage does not affect the path computed in the first stage and hence the name decoupled. The work done in computing the time optimal control along a specified path, i.e. the solution to the latter problem, includes that by Vukobratovic et al. 30] Shin et al.[27], Bobrow et al. 1] and Slotine et al. 28] Coupled approaches: These approaches do not go through the intermediate geometric path computation in the decoupled approaches. Even if they compute a geometric path they do not decouple the two stages the creation of the path and computing the ....

Shin, K.G. and McKay, N.D., "Minimum-time Control of Robotic Manipulators with Geometric Path Constraints ", IEEE Transactions on Automatic Control, Vol AC-25, 1985.

....cost of a search in the phase space of our system which is 6dimensional. Transforming a path into a trajectory is a classical problem in robotics. The minimal time parameterization of a given path has been mainly addressed for manipulators. Different methods have been proposed in this context [48], 4] 49] see [36] for an overview) Application to mobile robots appears in [47] the computation of a time optimal motion along a path is used to evaluate the cost of this path. The objective is to compute optimal trajectories for a mobile robot moving on a terrain. The problem is well ....

....constraints, our method deals with bounds on the velocities of the robot. This point has not been taken into account in prior work about time optimal parameterization (it is mentioned in [47] B. Constraints in the phase plane (s; s) In this section, we recall some key notions used in [4] [48], 49] and introduce some notation. Without loss of generality we consider now the case of a forward motion. By setting d v (s) q dxr ds (s) 2 dyr ds (s) 2 and d (s) d r ds (s) LAMIRAUX, SEKHAVAT AND LAUMOND: MOTION PLANNING AND CONTROL FOR HILARE PULLING A TRAILER 7 the ....

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K. Shin and N. Mc Kay, "Minimum-Time Control of a Robotic Manipulator with Geometric Path Constraints", IEEE Transactions on Automatic Control, Vol. 30 No. 6, 1985.

....scheme based on linearization of the robot dynamics to compute the optimal solution. Time optimal control is also an alternative for planning trajectories in the actuator space when the path in the joint space is obtained with other methods (see above) Bobrow et al. 13] and Shin and McKay [129] independently developed similar methods for computing the time optimal control for a serial manipulator moving along a given path. They showed that this problem is equivalent to time optimal control of a double integrator system and that the solution will thus be bang bang (the input is always ....

....this algorithm. Huang and McClamroch [59] adapted the method to contour following and found a solution for switching between free motion and constrained motion. Shiller and Lu [126] generalized the algorithm from [13] to handle singular trajectories. Dahl [32] extended the approaches from [13] and [129] to flexible manipulators. Theoretical results for time optimal control of mechanical linkages were derived in [1, 30, 135] Shiller and Dubowsky [128] proposed an algorithm for computing time optimal inputs and trajectories for a robot moving among obstacles. They approximated the trajectories ....

K. G. Shin and N. D. McKay. Minimum-time control of robotic manipulators with geometric constraints. IEEE Transactions on Automatic Control, AC-30(6):531--541, 1985.

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K.G.Shin and N.D.McKay. Minimum time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 1985.

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K. G. Shin and N. D. McKay. Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, AC-30(6):531--541, June 1985.

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Shin, K. G. and McKay, N. D. 1985. Minimum-time control of robotic manipulators with geometric path constraints.

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K. G. Shin and N. D. McKay, "Minimum-time control of robotic manipulators with geometric path constraints," IEEE Transactions on Automatic Control, vol. AC-30, no. 6, pp. 531--541, June 1985.

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K. G. Shin and N. D. Mckay, "Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints," IEEE Trans. Auto. Contr., vol. 30, no. 6, pp. 531541, 1985. Iterative Learning Control

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K.G. Shin and N.D. McKay, "Minimum-time control of robotic manipulators with geometric path constraints," IEEE Transaction on Automatic Control, vol. AC-30, no. 6, pp. 531--541, June 1985.

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K. G. Shin and N. D. McKay. Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 30(6):531-- 541, 1985. 114

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K. G. Shin and N. D. McKay. 1985. Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 30(6):531--541, June 1985.

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