| R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--555, 1999. |
....One of the contributions of the present paper is the extension of this idea of backchaining controllers to concurrent systems. 2.5 Compositional Control Preimage backchaining was introduced into the motion planning literature in [19] as a method of sequentially composing motion strategies. In [5] this method was extended to robot juggling in work that serves as the basis of our current research. The idea is to start with a palette of controllers Phi 1 ; Phi n for a robot. Suppose Phi k has domain D k and goal G k . Order the palette by setting Phi i Phi j (read Phi i prepares ....
Robert R. Burridge. Sequential Composition of Dynamically Dexterous Robot Behaviors. PhD thesis, University of Michigan, 1996.
....oriented so that both edges are in view (likewise with H 2 ) Now, de ne three image based controllers 0 : E 0 ; H 0 ) 1 : E 1 ; H 1 ) 2 : E 2 ; H 2 ) Note that the domains of attraction and goals of these controllers are shown in Table 1. Following Burridge et al. [1, 2] we say that controller i prepares controller j , written i j , if G( i ) 2 D( j ) In our case, we have 2 1 0 : 19) 7 D G 0 V 0 H 0 1 V 1 H 1 2 V 2 H 2 Table 1: This shows the domain of attraction and goal for each of the three controllers, 0 , ....
R. R. Burridge. Sequential Composition of Dynamically Dexterous Robot Behaviors. PhD thesis, The University of Michigan, Ann Arbor, MI, 1996.
.... formations [19] 20] 21] getting into formation [22] 23] 24] maintenance of formation shape [25] 26] 27] and switching between formations [28] 29] Approaches to modeling and solving these problems have been diverse, ranging from paradigms based on combining reactive behaviors [17] [30] to those based on leader follower graphs [25] and virtual structures [31] 32] In this paper we describe a suite of controllers and estimators and a methodology for their composition that permits control of formations for a group of robots in all the above and other applications. This suite ....
R. Burridge, A. Rizzi, and D. Koditschek, "Sequential composition of dynamically dexterous robot behaviors," Int. J. Robot. Research, vol. 18, no. 6, pp. 534--555, June 1999.
....aspirations [23] Despite their limited motion repertoires and rather deliberate movements, these robotic systems are truly engineering marvels. The work in [1] provides a good summary of behavioral architectures explored in the context of robotics. A 3 DOF ball juggling robot is described in [6] which uses a theory of behavior composition, although the practicality of extending the method to high DOF dynamic models of human motions is unclear. Computer animation is to a large extent unencumbered by the exacting fidelity requirements of biomechanical models and the mechanical limitations ....
R. R Burridge, A. A. Rizzi, and D. E Koditschek. Sequential composition of dynamically dexterous robot behaviors. The International Journal of Robotics Research, 18(6):534--555, June 1999.
....polygon impacting on a vertex. Atkeson and Schaal [28] developed a devil sticking robot which uses a memory based learning algorithm to learn a robust juggling strategy. Devil sticking is a demanding form of bat juggling two sticks are used to bat a third stick back and forth. Burridge et al. [29] study a hybrid control approach to juggling, catching, and palming a ball in three dimensions. Our robot juggles a puck floating on an inclined air table. Experimental and analytical studies on controlling the motion of an air hockey puck by impact are carried out in (Partridge and Spong [30] ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, "Sequential composition of dynamically dexterous robot behaviors," Int. J. Robot. Res., vol. 18, no. 6, pp. 534--555, June 1999.
....reproduced as follows: n 1 ; E n 1 ) f(x n ; y n ; x n ) 5.1) This is graphically depicted in Figure 5.1. A more planner centric view is to view the plan as a map from one trajectory to another: x n 1 ; y n 1 ; x n 1 ) P (x n ; y n ; x n ) 5. 2) This formulation was inspired by [BRK99] This map abstracts the details of the bounce itself and defines the local goal for every trajectory in the domain; successive trajectories presumably chain to the goal. The control action for each state is implicit in the successor state and may be computed by inverting the physical model. This ....
....is a transition between flights controlled by the leg angle and energy change E. The path shown has constant total energy so the hopper reaches approximately the same altitude even as the terrain drops away. on the planned sequence. This particular description of the problem was inspired by [BRK99] 5.2 Planning Issues This section enumerates the physical constraints on plans in order to motivate the planner design. The diagrams of Section 4.4 illustrate some of the physical constraints but are not sufficient to write a planner, and the planning formulation of the previous section offers ....
[Article contains additional citation context not shown here]
R.R. Burridge, A.A. Rizzi, and D.E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--55, June 1999.
.... Lyapunov functions is described in [11] An important contribution towards the application of multiple Lyapunov functions for practical controller design is the work in [12] and [13] The idea of guiding the system through a sequence of equilibrium points in order to stabilize it was employed in [14]. An assumption that is common to most of these works (an exception is [14] is that every subsystem has the same equilibrium point which has to be stabilized. However, hybrid systems can exhibit much richer behavior: the system might switch between multiple equilibrium sets before reaching the ....
.... the application of multiple Lyapunov functions for practical controller design is the work in [12] and [13] The idea of guiding the system through a sequence of equilibrium points in order to stabilize it was employed in [14] An assumption that is common to most of these works (an exception is [14]) is that every subsystem has the same equilibrium point which has to be stabilized. However, hybrid systems can exhibit much richer behavior: the system might switch between multiple equilibrium sets before reaching the final state. It is also commonly assumed that the switches between the ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, "Sequential composition of dynamically dexterous robot behaviors." Preprint, 1996.
....there is no need to actively drive the system into some designated region, as we do in the present paper. Stability of hybrid systems is also discussed in [11, 12] The idea of driving the system through a sequence of equilibrium points until a desired equilibrium point is reached was employed in [13]. In this work, the switch between di#erent controllers always occurs at an equilibrium point. The authors also assume that the region of attraction of each controller is known so there is no need for Lyapunov functions to prove the stability. In this paper, we are interested in systems that ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, "Sequential composition of dynamically dexterous robot behaviors." Preprint, 1996.
....no need to actively drive the system into some designated region, as we do in the present paper. An earlier work on stability of switching controllers is also [19] The idea of driving the system through a sequence of equilibrium points until a desired equilibrium point is reached was employed in [20]. In this work, the switch between di#erent controllers always occurs at an equilibrium point. The authors also assume that the region of attraction of each controller is known so there is no need for Lyapunov functions to prove the stability. The paper is organized as follows. We start with a ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, "Sequential composition of dynamically dexterous robot behaviors." Preprint, 1996.
....merely puts together , in a safe and correct way, to realize the assembly process. Such a palette of controllers is relatively easy to build for environments well described by generalized damper dynamics [12] but becomes quite challenging when dynamical dexterity is required. For example, in [2], substantial hand building affords deployments of controllers whose domains of attraction explicitly include portions of the forward limit sets of their neighbors. Here, we simply assume that these dynamical systems details have been worked out via parameterized families of regulators, and ....
....robot assembly, and hybrid discrete continuous systems including Petri Nets. We review each of these areas as they pertain to the present research. Preimage backchaining was introduced into the motion planning literature in [14] as a method of sequentially composing motion strategies. In [2] this method was extended to dynamically dexterous robot manipulators in work that serves as the basis of our current research. In [11] we expanded these ideas to include the notion of concurrent composition of behaviors for the case of several robots in a shared workspace based on simple Petri ....
Robert R. Burridge, Alfred A. Rizzi, and Daniel E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 1998.
....One of the contributions of the present paper is the extension of this idea of backchaining controllers to concurrent systems. 2.5 Compositional Control Preimage backchaining was introduced into the motion planning literature in [19] as a method of sequentially composing motion strategies. In [5] this method was extended to robot juggling in work that serves as the basis of our current research. The idea is to start with a palette of controllers Phi 1 ; Phi n for a robot. Suppose Phi k has domain D k and goal G k . Order the palette by setting Phi i Phi j (read Phi i prepares ....
Robert R. Burridge. Sequential Composition of Dynamically Dexterous Robot Behaviors. PhD thesis, University of Michigan, 1996.
....problem of solving a system of linear matrix inequalities. In [27] this ideas were used to derive a simplified test for stability of a hybrid system modeled with a Petri net. The idea of guiding the system through a sequence of equilibrium points in order to stabilize it was employed in [28]. An assumption that is common to most of these works (an exception is [28] is that every subsystem has the same equilibrium point which has to be stabilized. However, hybrid systems can exhibit much richer behavior: the system might switch between multiple equilibrium sets before reaching the ....
....this ideas were used to derive a simplified test for stability of a hybrid system modeled with a Petri net. The idea of guiding the system through a sequence of equilibrium points in order to stabilize it was employed in [28] An assumption that is common to most of these works (an exception is [28]) is that every subsystem has the same equilibrium point which has to be stabilized. However, hybrid systems can exhibit much richer behavior: the system might switch between multiple equilibrium sets before reaching the final state. Another common assumption is that the switches between the ....
[Article contains additional citation context not shown here]
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, "Sequential composition of dynamically dexterous robot behaviors." Preprint, 1996.
....to catch a ball thrown into the robot s workspace, where catching means bringing the ball to eventual standstill on the bat. By sequential composition of locally convergent controllers, one for each subregion in the state space of the ball, the ball can be caught from almost any initial state [3, 4]: When the ball is falling at high speeds, the controller switches to bouncing control to slow the ball down. At lower speeds, the controller may switch to palming behavior, where the bat is able to maintain contact with the ball continuously without bouncing. Ultimately, the ball is caught and ....
R. Burridge, A. Rizzi, and D. Koditschek. Sequential composition of dynamically dexterous robot behaviors. Int'l J. Robot. Res., 1997. To appear.
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Burridge R R, Rizzi A A, and Koditschek D E 1999 Sequential Composition of Dynamically Dexterous Robot Behaviors. Int. J. Rob. Res. 18(6):534 - 555.
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R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--555, 1999.
....will yield substandard results. Recently, hybrid control techniques have been used to move higher level decisions into the controller in a provably stable manner. Time varying system dynamics [1] state and control constraints [2, 3] disturbances [4] and task level programming of dynamic tasks [5] have been incorporated into controllers. The application discussed here concerns robotic couriers used for carrying product sub assemblies through a rapidly deployable assembly system called minifactory [6] The minifactory is composed of a series of tabletop sized platen tiles that form the ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, "Sequential composition of dynamically dexterous robot behaviors," International Journal of Robotics Research, vol. 18, pp. 534--555, June 1999.
....guide the transitions between controllers as well as to run the controllers, freeing the high level agent programs to deal with the more relevant and abstract problem of deciding what to do and how to do it. This notion of automatically managing the transition between controllers was introduced in [7], abstractly fit to the domain of minifactory in [8] and recently demonstrated experimentally [9] 2. Distributed Programming The distributed and cooperative nature of AAA has implications on the form of agent programs: an agent program is not simply a script, but rather defines an instance of ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--555, June 1999.
....These notions are described formally in the appendix. In Section 5.1 we will give a simple example of how such controllers can be designed. Once the control modes are designed, modes may be strung together in such a way that the goal of one controller is in the domain of the next, as in [6] where different juggling behaviors are composed. One of the contributions of the present paper is the extension of this idea of backchaining controllers to concurrent systems. 2.5 Compositional Control Preimage backchaining was introduced into the motion planning literature in [19] as a method ....
Robert R. Burridge, Alfred A. Rizzi, and Daniel E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. To appear, 1998.
....second author [11] which solves the latter problem. By an appropriate extension of that navigation function in the present context, convergence to the goal is guaranteed for all initial conditions in which the three feature points are visible. Using a sequential composition technique proposed in [2], this is extended to include all initial conditions in the camera s workspace. 2 Planar Rigid Body Servos Our stated objective is to design an IB visual servo system for control of a planar convex polygonal rigid body which directly minimizes the percieved error, such that all initial ....
....the goal G( For this controller, D( V and G( H . 2.3 Sequential Composition In this section, we use sequential composition to construct a hybrid global image based servo for a planar rigid body. A detailed and general procedure for applying sequential composition is outlined in [2], so we conclude for the sake of clarity with a simple example in which the rigid body is a triangle. The idea can easily be extended to a convex polygonal body with n edges. 2.3.1 Example: Triangular Body Consider a triangle with edges labeled E 0 ; E 1 ; E 2 , each of which has three ....
[Article contains additional citation context not shown here]
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. Int. J. Rob. Res., (to appear).
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R. Burridge, A. Rizzi, and D.E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534-55, 1999.
.... locally defined dynamics that realize single letter patterns. These act collectively as a toolbox from which to build a hybrid controller for achieving arbitrary patterns with a single AGV. This represents a slight generalization of the scheme the second author and colleagues have proposed in [4]. The problem of dynamics and control on non trivial graphs is then considered in 3, beginning with a detailed discussion of a natural intrinsic coordinate system in which to frame the configuration space. We present a topological analysis of the configuration space for a pair of AGV s on a ....
....that pattern if its M block extension eventually reaches the goal BBBBB . under the iterates of # M . In other words, after some finite number of applications of #,the excursion consists of repetitions of the block B (terminating possibly with the empty edge) In a previous paper [4], the second author and colleagues introduced a very simple but e#ective discrete event controller for regulating patterns on graphs from all reachable initial edges by pruning the graph back to a tree (imposing an ordering) Of course, this simple idea has a much longer history. In robotics it ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. Int. J. Rob. Res., (to appear).
....process can be ad hoc and frequently results in a large fraction of the control code being exception handler code . This cost is felt in terms of expensive programming projects, incompletely understood factory behavior, and a delay in the introduction of new products to the market. Burridge [1] et al. introduced backchaining as a way to sequentially compose closed loop robot behaviors in a safe and formal fashion. We believe that for this method to be useful in factory automation and other distributed robotics applications, it should be generalized to concurrent situations. The ....
....feedback controllers for which the methods developed here merely serve as glue. Such a palette of controllers is relatively easy to build for environments well described by generalized damper dynamics [7] but becomes quite challenging when dynaimcal dexterity is required. For example, in [1], substantial hand building affords deployments of controllers whose domains of attraction explicitly include portions of the forward limit sets of their neighbors. Here, we simply assume that these dynamical systems details have been worked out via parametrized families of regulators, and ....
[Article contains additional citation context not shown here]
Robert R. Burridge, Alfred A. Rizzi, and Daniel E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 1998.
....grant DMS 9971629 at the Georgia Institute of Technology. that can specify similarly goal oriented work exchange at any reasonable level of generality with any reasonable likelihood of successful implementation(much less, of formal verification) For reasons we have discussed elsewhere at length [7, 21], we construe task to mean any behavior that can be encoded as the limit set of the closed loop dynamical system resulting from coupling the robot up to its environment. By programming is meant (at the very least) a means of composing from extant primitive task behaviors new, more specialized, ....
....meant (at the very least) a means of composing from extant primitive task behaviors new, more specialized, or elaborate capabilities. A decade s research by the second author and colleagues has yielded the beginnings of a compositional methodology for tasks that can be encoded as point attractors [29, 28, 7, 14, 19]. In the present paper, we take the first steps toward a formal foundation for tasks that can be encoded as the next simplest class of steady state dynamical systems behavior limit cycles. 1.1 Contributions of the Paper In this paper we are able to prove for the first time the partial ....
[Article contains additional citation context not shown here]
R. Burridge, A. Rizzi, and D.E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534-- 55, 1999.
....controller. These notions are described formally in Appendix I. In Section 5.1 we will give a simple example of how such controllers can be designed. Once the control modes are designed, modes may be strung together in such a way that the goal of one controller is in the domain of the next, as in [6] where different juggling behaviors are composed. One of the contributions of the present paper is the extension of this idea of backchaining controllers to concurrent systems. 2.5 Compositional Control Preimage backchaining was introduced into the motion planning literature in [19] as a method ....
Robert R. Burridge, Alfred A. Rizzi, and Daniel E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. To appear, 1998.
....progress has been made on the development of new and more capable mechanisms, there has been only minimal progress at providing new paradigms for programming or instructing these mechanisms. The ideas presented here are complimentary to some early ideas on task level programming of dynamic tasks [2, 1], but focus instead on how collections of controllers can be used to simplify the task of programming the behavior of a generic mechanism. As a component of a long term project (minifactory 1 [5] which is focused on the development of modular robotic components and tools to support the rapid ....
.... that under the action of Phi i any state that starts in D( Phi i ) will be taken to G( Phi i ) without leaving the set D( Phi i ) We then say that controller Phi 1 prepares controller Phi 2 , denoted Phi 1 Phi 2 , if its goal lies within the domain of the second G( Phi 1 ) ae D( Phi 2 ) [1]. For an appropriately parameterized set of controllers, U , this relation induces a generally cyclic directed graph. Assuming that the overall goal, G, coincides with the goal of at least one controller, G( Phi i ) G, then by starting with Phi i and recursively tracing the relation backwards ....
[Article contains additional citation context not shown here]
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. submitted to the International Journal of Robotics Reaserch, 1996.
....or broadcasting its inability to proceed thus bringing the factory to an orderly stop. Although it is potentially difficult to guarantee this level of capability in an arbitrary system we feel that through judicious use of a combination of traditional AI reasoning [10] and reactive behaviors [2] that it can be achieved in the highly constrained domain of minifactory. 3.2.2 Factory Calibration Initialization Integral to the rapid deployment of an assembly system is the need for precise and automatic calibration and initialization whenever a factory is turned on. There are three ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. submitted to the International Journal of Robotics Reaserch, 1996.
....fault, or broadcasting its inability to proceed thus bringing the factory to an orderly stop. Although it is potentially difficult to guarantee this level of capability in an arbitrary agent we feel that through judicious use of a combination of traditional AI reasoning [7] and reactive behaviors [4] that it can be achieved in the highly constrained domain of minifactory. 4.2 Factory Calibration Initialization Integral to the rapid deployment of an assembly system is the need for precise and automatic calibration and initialization whenever a factory is turned on. There are three ....
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. submitted to the International Journal of Robotics Reaserch, August 1996.
....of parameterized controllers. The continuous layer may require high communications bandwidth, since often the states that it must monitor will be on other agents, and true real time operation is critical. This notion of automatically managing the transition between controllers was introduced in [2] and applied, theoretically, to the domain of minifactory in [6] The programs written by the user and downloaded to the agent form the upper half of this program hierarchy. The lower half is hard coded in the form of a palette of real time control strategies and a manager which executes them ....
.... that under the action of Phi i any state that starts in D( Phi i ) will be taken to G( Phi i ) without leaving the set D( Phi i ) We then say that controller Phi 1 prepares controller Phi 2 , denoted Phi 1 Phi 2 , if its goal lies within the domain of the second G( Phi 1 ) ae D( Phi 2 ) [2, 6]. For an appropriately parameterized set of controllers, U , this relation induces a generally cyclic directed graph. Assuming that the overall goal, G, coincides with the goal of at least one controller, G( Phi i ) G, then by starting with Phi i and recursively tracing the relation backwards ....
[Article contains additional citation context not shown here]
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 1998. (to appear).
....of the state space) in the cover, and connecting arcs denote non empty intersection. Dynamically induced movement along the graph corresponds to the construction of vector fields whose flow brings an entire cell into into its intersection with the adjacent cell to be visited. For example, in [9], the second author and colleagues define a prepares relation a partial order that prunes this graph into a tree via controllers with point attractors in a specified neighborhood whose domain of attraction includes the entire cell (which is also positive invariant) We will in fact adopt ....
.... locally defined dynamics that realize single letter patterns. These act collectively as a toolbox from which to build a hybrid controller for achieving arbitrary patterns with a single AGV. This represents a slight generalization of the scheme the second author and colleagues have proposed in [9]. In x3, we turn to the problem of introducing multiple AGV s in the context of graphs which are manifolds. In this simpler case, it is often, but not always, possible to interleave controllers for single AGV s into a safe controller on the product configuration space. The problem of dynamics and ....
[Article contains additional citation context not shown here]
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. Int. J. Rob. Res., (to appear).
No context found.
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--555, 1999.
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R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behavious. Int. J. Robot. Res., 18(6):534--555, 1999.
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R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. Int. J. Robot. Res., 18(6):534-555, 1999.
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Burridge, R.R., Rizzi, A.A., Koditschek, D.E.: Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research 18 (1999) 534---555
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R. Burridge, A. Rizzi, and D. Koditschek, "Sequential composition of dynamically dexterous robot behaviors," Int. J. Robot. Res., vol. 18, no. 6, pp. 534--555, June 1999.
No context found.
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. Int. J. Robot. Res., 18(6):534--555, 1999.
No context found.
R. R. Burridge, A. A. Rizzi, and D. E. Koditscheck, "Sequential composition of dynamically dexterous robot behaviors." Int. J. Rob. Res., vol. 18(6), pp. 534--555, 1999.
No context found.
R. R. Burridge, A. A. Rizzi, and D. E. Koditscheck, "Sequential composition of dynamically dexterous robot behaviors." Int. J. Rob. Res., vol. 18(6), pp. 534--555, 1999.
No context found.
Robert R. Burridge, Alfred A. Rizzi, and Daniel E. Koditschek, Sequential composition of dynamically dexterous robot behaviors, Int. J. Rob. Res. 18 (1999), no. 6, 534--555.
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R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. The International Journal of Robotics Research, 18(6):534--555, June 1999.
No context found.
R. Burridge, A. Rizzi, and D. Koditschek, "Sequential composition of dynamically dexterous robot behaviors," Int. J. Robot. Research, vol. 18, no. 6, pp. 534--555, June 1999.
No context found.
R. Burridge, Rizzi A., and D. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--555, June 1999.
No context found.
R. Burridge, Rizzi A., and D. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534--555, June 1999.
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