D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(des situations dans lequelles on pr evoit que le robot ne fonctionnera pas correctement) Cela suppose la connaissance pr ealable d un mod ele ad equat du robot ou l inf erence de ce dernier. Il existe des techniques d apprentissage permettant d elaborer un controleur de robot a partir de tests [3]. Ces derni eres pr esentent des r esultats int eressants jusqu a un certain point. Mais les mod eles elabor es (r eseaux de neurones, par exemple) ne conviennent pas a la d eduction de tests pertinents. En fait, en robotique, les techniques d apprentissage ont surtout et e employ ees en vue ....

D. Luzeaux. How to deal with robot motion? Application to car-like robots, UCBERL -M92-7, Berkeley, USA, January 1992.

....time, one of them is fired, and the system reacts instinctively to each little variation of the external world. This kind of control has been applied successfully to a 5kW laser robot for metal plaque cutting [20] and on simulated mobile robots: parking maneuvers (cars and trucks with trailers [9, 12]) and driving a car on a track [13] The efficiency of rule based incremental con trol in terms of stability, trajectory tracking for linear and nonlinear systems, robustness has been proved [10, 12] Therefore we know that kind of control works and we can turn with confidence to the delicate ....

D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.

.... help of computers necessarily involves only a finite number of bits to encode any real value, hence there is only a finite total number of values (commands correspond to physical actuators and are obviously bounded) The second definition introduces incremental control which has been studied in [Luz92b, Luz92c, LZ93] in terms of theoretical and practical efficiency. 2.1 Examples First, we give the example of a class of control problems such that the information which is carried by the vector state only indicates whether the system is in a failure situation (x k = 1) or not (x k = 0) More precisely, let h be ....

D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.

....with the state equation: X k 1 = f(X k ) g(X k )U k , where X k are the n dimensional states, U k the p dimensional inputs, and f and g are two differentiable functions modeling respectively the drift and the nonholonomy of the system. This class of system covers many models used in robotics [4, 9, 10, 11]. Given a desired trajectory (i.e. a sequence X (d) k ) and nominal inputs (a sequence U (d) k yielding this trajectory) in order to find a rule based incremental control law that stabilizes the system, we compute first the linearization of the system around this desired trajectory, and ....

D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.

....the same mould ; while depending on quite different concepts, they are basically similar. 1 Introduction The study we set out is motivated by a wish to theoretically justify the processes implemented in the program Candide, which aim is to find a set of rules to control any system, by learning [1, 3]. Incremental control and recursive learning ( recursive is to be understood in its non technical sense) are two main features of this program. From a theoretical point of view, both concepts reveal recursive aspects (and this time in a technical sense) that lead to non trivial results ; ....

....0; 1g; ffl 0 k 2 f Gammam; Delta Delta Delta ; mg, and Delta; Delta 0 are two positive real numbers. The coefficients ffl i k and ffl 0 k will be called signs and the set of their values at time k is the sign policy. Such control laws are called (n; m) incremental control laws [3]. This equation may be rewritten as : u k = u k Gamma1 v k ffl k Delta 0 . The real number Delta 0 is a given increment and the integer ffl 0 k (bounded by m) tells the amount of the action at time k. This part of the equation models the increase, decrease or leave part. The term v k ....

D. Luzeaux. How to deal with robot motion? application to car-like robots. Technical report, Memorandum No. UCB/ERL M92/7, 1992.

....the very high number of maneuvers involved. This is why we had to look for rule based incremental controllers which will lead to much less maneuvers. 2. 2 Parking a car and a truck with a trailer 1 body robot: Different rule based incremental control laws have already been given in [Luz92b, LZ92, Luz92a] We explain briefly here how one of these works. It can be expressed by a set of 10 rules: r0 reverses the car till the rear of the car arrives at the height of the parking place. r1 et r2 are fired during the first maneuver: the right rear of the car has to reach the right rear part of the ....

....of the rear axis of the first body and the midpoint of the rear axis of the second body, and v the speed of the midpoint of the front axis of the first body. We assume that jvj is constant. Figure 2: Parking a car(left) and a truck with trailer (right) A qualitative study of these equations in [Luz92a] shows how to write a rule based incremental control law. Figure 2 illustrates such a law. The main idea is to drive the trailer into the parking place (when starting parallelly to the parking place, just back up, turn slightly once to the right and once to the left) and then to translate the ....

[Article contains additional citation context not shown here]

D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.

....adaptive fuzzy control or self organizing fuzzy control [HMB93] which relies on fuzzy sets to model inputs and outputs and a learning procedure that adapts parameters of these sets and their laws of composition. 5 Rule based incremental control and the learning program Candide As discussed in [Luz92a, Luz92b, Luz94b, Luz95, LM96] a rule based incremental control law is defined by: u k 1 = u k ffl k Delta ffl k = y k ; Delta Delta Delta ; y k Gammar ) with: Delta 2 R ; computable; ffl k 2 f Gammam; Gammam 1; Delta Delta Delta ; Gamma1; 0; 1; Delta Delta Delta ....

D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.

....will be increased, that one will be decreased or left untouched. The preceding discussion is entirely informal and does not pretend to have found the behavior model of any human; it is only based on various experiments (cutting metal plaques with a laser robot [FKB 85] driving a car [Fou90, Luz92a] landing a plane [HLG91] The formal tool resulting from that discussion is rule based incremental control [Luz91] An incremental control law relates u k 1 to u k by: u k 1 = u k ffl k Delta where Delta is a non null positive real and ffl k is an integer in f Gammam; Delta Delta ....

.... assumptions [Luz92b] ffl the range of ffl k depends on the system to control; some necessary inferior bounds are given in [Luz91] ffl car like mobile robots can be completely controlled by rule based incremental controllers in any connected environment with any distribution of obstacles [Luz92a] Thus incremental control provides us with an efficient tool within control theory; furthermore its expression is easy enough to comply with learning principles. 3 A framework for learning in control Our aim is to show that in a situation of the kind described before, the concept of stage ....

D. Luzeaux. How to deal with robot motion? Application to car-like robots. Technical report, University of California at Berkeley, No UCB-ERL-M92-7, 1992.

....give in the paper the learning methodology and show how Candide learned to drive a car. 2 Incremental rule based control laws These control laws, whose mathematical formulation follows, have been studied experimentally during the last years [1, 4, 2] however theoretical results are very recent [6, 7]. 2.1 Theoretical results The incremental rule based control laws have the following form: If output in this range then increase, decrease or leave the input The input u k at time k is related to the input u k Gamma1 at time k Gamma 1 by the equation: 8 : u k = u ....

....between two time steps are to increase, to decrease by an increment or to keep the current value of each command; this means turning the steering wheel and performing backups and forward drives, but no correction on the speed is done. This parking allows an unlimited number of maneuvers. In [7], we show furthermore that a car like robot is completely controllable by rule based incremental control laws, i.e. we can find such a law that brings the robot from any configuration to any configuration even amidst obstacles. Such laws have also been used to park a truck with one trailer [7] 3 ....

[Article contains additional citation context not shown here]

D. Luzeaux. How to deal with robot motion, application to car-like robots. Technical report, University of California at Berkeley, 1992.

....easiest law: the only admissible actions are either to increase, to decrease by an increment or to leave unchanged the last input. Actually, in all these propositions, the sign policy only depends upon the initial state and X k , as can be seen in [Luz91] A stronger result holds, as is proved in [Luz92], where a real state feedback law is considered (the sign ffl k depends explicitly on the value of X k ) Proposition 5 For a controllable linear SISO system (X k 1 = AX k Bu k ) a given desired trajectory (X (d) k ) k2N and a sequence of inputs (u (d) k ) k2N yielding this trajectory ....

....between the initial and the final configuration is a compact in C free (the free configuration space, i.e. the complement of the union of C obstacles) and can thus be covered by a finite number of balls. This completes the sketch of the proof of the full controllability (for a detailed proof, see [Luz92]. Proposition 6 Let q and q 0 be two configurations in the same component of C free . For any neighborhood of q , there exists a feasible free path between q and a configuration in this neighborhood, that can be obtained by a rule based incremental controller. Of course this constructive proof ....

[Article contains additional citation context not shown here]

D. Luzeaux. How to deal with robot motion? application to car-like robots. Technical report, University of California, No UCB-ERL-M92-7, 1992.

.... the procedure which yields the correct inputs in order to achieve the desired outputs is a mechanical procedure (a computable function) ffl there exists an enumeration of all such procedures With these assumptions it is still possible to prove that a very large class of systems can be controlled [2, 3, 4]. Some terminology can be useful: the procedure that yields the inputs is called a controller and it will be expressed as a finite set of if then rules: the if part models the current situation (a formal development of these ideas, as it can be found in the references, uses actually the concept of ....

D. Luzeaux, (1992), How to deal with robot motion? Application to car-like robots, University of California at Berkeley, No UCB-ERL-M92-7.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC