François G. Pin

Time optimal trajectories for mobile robots with two independently driven wheels

This article addresses the problem of time-optimal motions for a mobile platform in a planar environment. The platform has two nonsteerable, independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations, assuming an unobstructed environment. Using Pontryagins maximum principle (PMP), we formally demonstrate that all time-optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the acceleration on each wheel is at either its upper or its lower limit). The PMP, however, provides only the conditions necessary for time optimality. To find the time- optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this param eterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numer ically that robot trajectories with three switch times (two on one wheel and one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving sim ilar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters and consist of subsets of trajec tories with three switch times (for the problem when the final orientation of the robot is not specified) or four switch times (when a full final configuration is specified). We conclude with a description of the use of the method for trajectory planning for one of our robots and discuss some comparisons of sample time-optimal paths with minimum length paths.

Design of an omnidirectional and holonomic wheeled platform prototype

The authors present the concepts for a new family of wheeled platforms which feature full omnidirectionality with simultaneous and independent rotational and translational motion capabilities. They first describe the original orthogonal-wheels assembly on which these platforms are based and discuss how a combination of these assemblies is used to generate an omnidirectional capability. The design and control of a prototype platform developed to test and demonstrate the proposed concepts are then described, and experimental results illustrating the full omnidirectionality of the platform with decoupled rotational and translational degrees of freedom are presented.<<ETX>>

Autonomous mobile robot navigation and learning

Research focused on the development and experimental validation of intelligent control techniques for autonomous mobile robots able to plan and perform a variety of assigned tasks in unstructured environments is presented. In particular, an autonomous mobile robot, HERMIES-IIB intelligence experiment series, is described. It is a self-powered, wheel-driven platform containing an onboard 16-node Ncube hypercube parallel processor interfaced to effectors and sensors through a VME-based system containing a Motorola 68020 processor, a phased sonar array, dual manipulator arms, and multiple cameras. Research on navigation and learning is examined.<<ETX>>

Autonomous navigation of a mobile robot using custom-designed qualitative reasoning VLSI chips and boards

Two types of computer boards including custom-designed VLSI chips have been developed to add a qualitative reasoning capability to the real-time control of autonomous mobile robots. The design and operation of these boards are first described, and an example of their use for the autonomous navigation of a mobile robot is presented. The development of qualitative reasoning schemes emulating human-like navigation in a priori unknown environments is discussed. The efficiency of such schemes, which can consist of as little as a dozen qualitative rules, is illustrated in experiments involving an autonomous mobile robot navigating on the basis of very sparse and inaccurate sensor data.<<ETX>>

Optimal positioning of combined mobile platform-manipulator systems for material handling tasks

Mobile manipulators are attracting significant interest in the industrial, military, and public service communities because of the potential they provide for increased efficiency in material handling and manipulation tasks. Corresponding interest has arisen in the robotics research community since the combination and coordination of the mobility of an autonomous platform with the robotic motion of a manipulator introduce complex analytical problems. One such problem arises from the particular kinematic redundancy which characterizes practical mobile manipulators. This paper is concerned with a particular aspect of the resolution of this redundancy, which is its utilization to optimize the systems position and configuration during task commutations when changes occur in both task requirements and task constraints. Basic optimization schemes are developed for cases when load and position constraints are applied at the end-effector. Various optimization criteria are investigated for task requirements including obstacle avoidance, maneuverability and several torque functions. The problem of optimally positioning the platform for execution of a manipulation task requiring a given reach is also treated. Emphasis is then placed on the multi-criteria optimization methods which are necessary to calculate the commutation configurations in sequences of tasks with varying requirements. Sample results are presented for a system involving a three-link planar manipulator on a mobile platform. The various optimization schemes are discussed and compared, and several directions (in particular the novel use of minimax optimization pioneered here for redundancy resolution) are outlined for further extensions of the methods to the general problem of motion planning and control of redundant robotic systems with combined mobility and manipulation capabilities.

Using Custom-designed Vlsi Fuzzy Inferencing Chips For The Autonomous Navigation Of A Mobile Robot

An approach merging the concepts of fuzzy logic and sensor-based behaviors has been developed to add a qualitative reasoning capability to the real-time control of autonomous mobile robots. The approach is implemented using custom-designed computer boards which include recently developed VLSI fuzzy inferencing chips. The design and operation of these boards are first described and an example of their use for the autonomous navigation of a mobile robot is presented. The development of qualitative reasoning schemes emulating human- like navigation in a-priori unknown environments is discussed. The approach using superposition of elemental sensor-based behaviors expressed in the fizzy Sets theoretic framework is shown to allow easy development and testing of the inferencing rule base, while providing for progressive addition of behaviors to resolve situations of increasing complexity. The efficiency of such schemes, which can consist of as little as a dozen qualitative rules, is illustrated in experiments involving an autonomous mobile robot navigating on the basis of very sparse and inaccurate sensor data.

Multi-criteria position and configuration optimization for redundant platform/manipulator systems

An important characteristic of practical mobile manipulators, i.e. manipulators mounted on mobile platforms, is their particular kinematic redundancy created by the addition of the degrees of freedom of the platform to those of the manipulator. This paper is concerned with the resolution of this kinematic redundancy, and in particular with the local optimization of the position and configuration of the system during task commutations when changes occur in both task requirements and task constraints. Optimization criteria for obstacle avoidance, manipulability, least torque norm and maximum actuator torque are first discussed. Emphasis is then placed on optimization methods for problems involving multi-requirements and multicriteria optimization. Sample results of the methods for a system including a three-link manipulator mounted on a mobile platform are presented and discussed.<<ETX>>

Using fuzzy behaviors for the outdoor navigation of a car with low-resolution sensors

An approach using superposition of elemental fuzzy behaviors to emulate humanlike qualitative reasoning schemes is discussed. The authors describe how a previously developed navigation scheme implemented on custom-designed VLSI fuzzy inferencing boards for indoor navigation of a small laboratory-type robot was progressively enhanced and used to investigate two control modes for driving a car in a priori unknown environments on the basis of sparse and imprecise sensor data. In the first mode, the car navigates fully autonomously, whereas in the second mode, the system acts as a drivers aid providing the driver with linguistic (fuzzy) commands, depending on the obstacles perceived by the sensors. Experiments with both modes of control are described in which the system uses only three acoustic range (sonar) sensor channels. Simulation results, as well as indoors and outdoors experiments, are presented and discussed.<<ETX>>

Motion planning for mobile manipulators with a non-holonomic constraint using the FSP (full space parameterization) method

The efficient utilization of the motion capabilities of mobile manipulators, i.e., manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (DOF) of the platform to those of the manipulator. At the velocity level, the linearized Jacobian equation for such a redundant system represents an underspecified system of algebraic equations, which can be subject to a varying set of contraints such as a non-holonomic constraint on the platform motion, obstacles in the workspace, and various limits on the joint motions. A method, which we named the Full Space Parameterization (FSP), has recently been developed to resolve such underspecified systems with constraints that may vary in time and in number during a single trajectory. In this article, we first review the principles of the FSP and give analytical solutions for constrained motion cases with a general optimization criterion for resolving the redundancy. We then focus on the solutions to (1) the problem introduced by the combined use of prismatic and revolute joints (a common occurrence in practical mobile manipulators), which makes the dimensions of the joint displacement vector components non-homogeneous, and (2) the treatment of a non-holonomic constraint on the platform motion. Sample implementations on several large-payload mobile manipulators with up to 11 DOF are discussed. Comparative trajectories involving combined motions of the platform and manipulator for problems with obstacle and joint limit constraints, and with non-holonomic contraints on the platform motions, are presented to illustrate the use and efficiency of the FSP approach in complex motion planning problems.

Navigation of car-like mobile robots in obstructed environments using convex polygonal cells

Abstract Due to their kinematics, car-like mobile robots cannot follow an arbitrary path. Besides obstacle avoidance, the path planning problem for such platforms has to satisfy two additional constraints: a lower bounded radius of turn and a non-holonomic constraint. When the robot is not circular, precise manuevering always implies working in the configuration space of the vehicle. Due to the complexity of representing this space, the planning of a path typically involves computer intensive methods, and rarely allows for real-time applications. In environments described with two-dimensional convex polygonal cells, we show that maneuvering can be completely handled with geometric reasoning. Within a convex cell, joining any two configurations of the vehicle only requires computation of maneuvers related to the beginning and the end of the trajectory. Just a few boundary configurations have to be checked to avoid collision. Because of the convexity of the cell, maneuvers related to the initial configuration and to the final configuration can be connected by a straight trajectory. This geometric reasoning approach allows not only precise calculation of the trajectories within the convex cells, but also extremely fast path-planning computation since it avoids representation of the whole configuration space. In generatl environments, a graph connecting adjacent convex cells is generated. To find a path between two distant configurations, the graph is searched to identify the cells that have to be traversed. Intermediate configurations are computed at the boundary of adjacent cells and the trajectory planning algorithm is applied to each set of consecutive configurations. Finally, the trajectories generated inside each cell are assembled to produce global collision-free paths in complex environments.