Two Vision-guided vehicles: temporal coordination using nonlinear dynamical systems Cristina P. Santos and Manuel Ferreira Abstract— This article addresses the problem of generating timed trajectories and temporally coordinated movements for two wheeled vehicles, when relatively low-level, noisy sensorial information is used to steer action. The generated trajectories have controlled and stable timing (limit cycle type solutions). Incoupling of sensory information enables sensor driven termi- nation of movement. We build on a previously proposed solu- tion in which timed trajectories and sequences of movements were generated as attractor solutions of dynamic systems. We present a novel system composed of two coupled dynamical architectures that temporally coordinate the solutions of these dynamical systems. The coupled dynamics enable synchroniza- tion of the different components providing an independence relatively to the specification of their individual parameters. We apply this architecture to generate temporally coordi- nated trajectories for two vision-guided mobile robots in a non-structured simulated environment, whose goal is to reach a target within a certain time independently of the environment configuration or the distance to the target. The results illustrate the robustness of the proposed decision-making mechanism and show that the two vehicles are temporal coordinated: if a robot movement is affected by the environment configuration such that it will take longer to reach the target, the control level coordinates the two robots such that they terminate approximately simultaneously. I. INTRODUCTION Trajectory planning has been extensively studied over the last few years, ranging from the addition of the time dimension to the robot’s configuration space [1], visibility graph [2], cell decomposition [3] or neural networks [4]. There are several results for time-optimal trajectory planning [5]. Despite the efficient planning algorithms that have been developed and the advances in the control domain which validated dynamic, robust and adaptive control techniques, the path planning problem in autonomous robotics remains separated in theory from perception and control. This sep- aration implies that space and time constraints on robot motion must be known before hand with the high degree of precision typically required for non-autonomous robot operation. In order to develop autonomous robot systems capable of operating in changing and uncertain environments it is required a tight coupling of planning, sensing and execution. However, timing is more difficult to control when it must be compatible with the requirement of continuous coupling to sensory information. Some approaches have addressed this issue [6], but timing was not fully explored. Industrial Electronics Department, University of Minho, Guimaraes, Por- tugal cristina@dei.uminho.pt, mjf@dei.uminho.pt In this article, we propose an approach fully formulated in terms of nonlinear dynamical systems which lead to a flexible timed behavior stably adapted to changing online sensory information. Dynamical systems have various desir- able properties which makes them interesting and powerful for trajectory generation. See [7], [8], [9], [10], [11], [12] for related work. First, the structural robustness of the solutions implies intrinsic robustness against small perturbations and noise and the possibility to fuse new inputs into the system without completely destroying its properties. Second, the low computation cost is well-suited for real time. Other properties are the smooth online modulation of the trajectories through changes in the parameters of the dynamical systems; the possibility to synchronize with external signals and to add sensory feedback pathways. The dynamics of the system globally encode a task (i.e. the whole attractor landscape) with the goal state as the point attractor. This is a ”always online” property, i.e., once a task is encoded into a dynamical system (e.g. learning) it will be always active, and no discrete trials are needed. Once properly designed, the dynamical system can be robust enough against perturbations and able to smoothly recover from perturbations by means of coupling terms in the dynamics. Another particularity is that these systems produce coordinated multidimensional rhythms of motor activity, under the control of simple input signals. Such systems are deemed to strongly reduce the dimensionality of the control problem. We build on previous work [13], [11], [14], where we proposed a dynamical system architecture that gen- erated timed trajectories, including rhythmic and discrete movement, movement sequences and temporally coordinated movements. The model consists of a dynamical system composed of stable fixed points and a stable limit cycle (an Hopf oscillator). Trajectories are generated through the sequencing of these primitives, in which the limit cycle is activated over limited time intervals. This sequencing is controlled by a “neural” competitive dynamics. By control- ling the timing of a limit cycle, the system performs well tasks with complex timing constraints. The online linkage to noisy sensorial information, was achieved through the coupling of these dynamical systems to time-varying sen- sory information [14], [13]. In [13], this architecture was implemented in a real vehicle and integrated with other dynamical architectures which do not explicitly parameterize timing requirements. In [11], we have generated temporally coordinated movements among two PUMA arms by coupling two such dynamical systems. In this work, coordination is modeled through mutual 2007 IEEE International Conference on Robotics and Automation Roma, Italy, 10-14 April 2007 WeA1.3 1-4244-0602-1/07/$20.00 ©2007 IEEE. 14