TechTalks from event: Technical session talks from ICRA 2012

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Non-Holonomic Motion Planning

  • Model Predictive Navigation for Position and Orientation Control of Nonholonomic Vehicles Authors: Karydis, Konstantinos; Valbuena, Luis; Tanner, Herbert G.
    In this paper we consider a nonholonomic system in the form of a unicycle and steer it to the origin so that both position and orientation converge to zero while avoiding obstacles. We introduce an artificial reference field, propose a discontinuous control policy consisting of a receding horizon strategy and implement the resulting field-based controller in a way that theoretically guarantees for collision avoidance; convergence of both position and orientation can also be established. The analysis integrates an invariance principle for differential inclusions with model predictive control. In this approach there is no need for the terminal cost in receding horizon optimization to be a positive definite function.
  • Regularity Properties and Deformation of Wheeled Robots Trajectories Authors: Pham, Quang-Cuong; Nakamura, Yoshihiko
    Our contribution in this article is twofold. First, we identify the regularity properties of the trajectories of planar wheeled mobile robots. By regularity properties of a trajectory we mean whether this trajectory, or a function computed from it, belongs to a certain class <i>C<sup>n</sup></i> (the class of functions that are differentiable <i>n</i> times with a continuous <i>n</i><sup>th</sup> derivative). We show that, under some generic assumptions about the rotation and steering velocities of the wheels, any non-degenerate wheeled robot belongs to one of the two following classes. Class I comprises those robots whose admissible trajectories in the plane are <i>C</i><sup>1</sup> and piecewise <i>C</i><sup>2</sup>; and class II comprises those robots whose admissible trajectories are <i>C</i><sup>1</sup>, piecewise <i>C</i><sup>2</sup> and, in addition, curvature-continuous. Second, based on this characterization, we derive new feedback control and gap filling algorithms for wheeled mobile robots using the recently-developed affine trajectory deformation framework.
  • A Homicidal Differential Drive Robot Authors: Ruiz, Ubaldo; Murrieta-Cid, Rafael
    In this paper, we consider the problem of capturing an omnidirectional evader using a Differential Drive Robot in an obstacle free environment. At the beginning of the game the evader is at a distance L>l from the pursuer. The pursuer goal is to get closer from the evader than the capture distance l. The goal of the evader is to keep the pursuer at all time farther from it than this capture distance. In this paper, we found closed-form representations of the motion primitives and time-optimal strategies for each player. These strategies are in Nash Equilibrium, meaning that any unilateral deviation of each player from these strategies does not provide to such player benefit toward the goal of winning the game. We also present the condition defining the winner of the game and we construct a solution over the entire reduced space.
  • On the Dynamic Model and Motion Planning for a Class of Spherical Rolling Robots Authors: Svinin, Mikhail; Yamamoto, Motoji
    The paper deals with the dynamics and motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits non-holonomic constraints to propel the rolling carrier. The full mathematical model as well as its reduced version are derived, and the inverse dynamics is addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two orthogonal axes of the actuation the condition of dynamic realizability of a feasible kinematic trajectory is established. The implication of this condition to motion planning in dynamic formulation is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere surface the dynamically realizable trajectories are essentially different from those resulted from kinematic models.
  • Control of Nonprehensile Rolling Manipulation: Balancing a Disk on a Disk Authors: Ryu, Ji-Chul; Ruggiero, Fabio; Lynch, Kevin
    This paper presents stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We use backstepping to derive a control law yielding global asymptotic stability. We present simulation as well as experimental results demonstrating the controller.
  • Estimating Probability of Collision for Safe Motion Planning under Gaussian Motion and Sensing Uncertainty Authors: Patil, Sachin; van den Berg, Jur; Alterovitz, Ron
    We present a fast, analytical method for estimating the probability of collision of a motion plan for a mobile robot operating under the assumptions of Gaussian motion and sensing uncertainty. Estimating the probability of collision is an integral step in many algorithms for motion planning under uncertainty and is crucial for characterizing the safety of motion plans. Our method is computationally fast, enabling its use in online motion planning, and provides conservative estimates to promote safety. To improve accuracy, we use a novel method to truncate estimated a priori state distributions to account for the fact that the probability of collision at each stage along a plan is conditioned on the previous stages being collision free. Our method can be directly applied within a variety of existing motion planners to improve their performance and the quality of computed plans. We apply our method to a car-like mobile robot with second order dynamics and to a steerable medical needle in 3D and demonstrate that our method for estimating the probability of collision is orders of magnitude faster than naive Monte Carlo sampling methods and reduces estimation error by more than 25% compared to prior methods.