Tomohide Naniwa

Robustness of P-type learning control with a forgetting factor for robotic motions

A class of simple learning control algorithms with a forgetting factor and a long-term memory and without use of the derivative of velocity signals is proposed for motion control of robot manipulators. The robustness of search learning laws with respect to initialization errors, fluctuations of the dynamics, and measurement noises is studied extensively. As a result the uniform boundedness of motion trajectories is proved based on the passivity analysis of robot dynamics. It is also proved that motion trajectories converge to a neighborhood of the desired one and eventually remain in it provided the content of the long-term memory is refreshed adequately after a sufficient number of trials.<<ETX>>

Model-based adaptive hybrid control for geometrically constrained robots

A model-based adaptive controller for robot manipulators under geometric endpoint constraint is proposed. It is based on joint-space orthogonalization of feedback signals. The adaptive law is devised by referring to the basic properties of robot dynamics, which are passivity of robot dynamics, use of feedback of residual error velocity and position signals that are projected to the tangent plane in joint space and orthogonal to the joint force vector caused by the contact, and use of the fact that important but uncertain physical parameters enter linearly in the equation of motion of robots. The convergence of tracking errors on the surface is proved under an appropriate initial condition and the smoothness of the surface. The convergence of force error is proved provided that the endpoint is kept in contact with the surface.<<ETX>>

Adaptive model-based hybrid control of geometrically constrained robot arms

This paper reports comparative experiments with a new model-based adaptive force control algorithm for robot arms. This controller provides simultaneous position and force trajectory tracking of a robot arm whose tool tip is in point contact with a smooth rigid surface. The algorithm is provably stable with respect to the commonly accepted rigid-body nonlinear dynamical model for robot arms. Comparative experiments show the new adaptive model-based controller to provide performance superior to that of both nonmodel-based controllers and nonadaptive controllers over a wide range of operating conditions.

A quadtree‐based path‐planning algorithm for a mobile robot

To enable a mobile robot to select automatically a collision-free path in a given workspace, design of a path-planning algorithm which must work efficiently in real-time is crucial. This article proposes a path-planning algorithm that selects a reasonable collision-free path tying start and goal points out of a quadtree representation of the robot workspace. The quadtree is obtained from fast conversion of a real image taken through a camera on the ceiling. It represents obstacles and their allocation in the workspace in good time and hence the algorithm is able to find a collision-free path while following the change of obstacles and their allocation. The algorithm is designed on the basis of “small-is-quick” principle. That is, the smaller a search space of the algorithm is, the faster the algorithm selects the shortest path out of the search space. To put the principle in practice, the algorithm investigates a path graph instead of the quadtree while spreading the path graph on the quadtree as small as possible, and selects fast the shortest collision-free path out of the path graph as a reasonable collision-free path. Thus the algorithm fulfils its function fast even in a workspace that has a number of obstacles with complicated shape. In comparison with several conventional path-planning algorithms presented so far, it is shown from experimental results that the proposed algorithm selects faster a reasonable collision-free robot path than others.

Selective learning with a forgetting factor for robotic motion control

A class of learning control algorithms with a forgetting factor 1> alpha >0 and without differentiation of velocity signals is proposed, which updates the input by u/sub k+1/=(1- alpha ) u/sub k/+ alpha u/sub 0/+ Phi e/sub k/, where u/sub k/ and e/sub k/ stand for command input and velocity error at kth exercise, respectively. The robustness of this learning control with respect to reinitialization errors, fluctuation of dynamics, and measurement noise is studied. It is shown that the exponential passivity of displacement robot dynamics plays a crucial role in the uniform boundedness of transient behaviors and the convergence in the progress of learning. A method called selective learning, which updates u/sub 0/ in the long-term memory by selecting the best command among the past several trials, is proposed. It is claimed that this method accelerates the speed of convergence.<<ETX>>

A practical algorithm for planning collision-free coordinated motion of multiple mobile robots

When multiple mobile robots are working in the same environment, planning of collision-free coordinated motion is necessary; here, an algorithm for planning such a motion of two mobile robots, no matter how crude the constraints of obstacles are, is proposed. The situation is modeled as a Petri net, which is considered as a useful model for describing and analyzing a system in which it is possible for some events to occur concurrently but there are constraints on the concurrence. In the Petri net, all motion constraints of robots in their paths are arranged as its firing rules, and hence collision-free coordination between the robots can be easily planning by manipulation of the firing rules. The algorithm always finds a collision-free coordinated path of two robots if there actually exists such a path in the environment. Moreover, because the algorithm does not use any knowledge of movement of the robots, precise time-varying trajectory control is not required and realization of the coordination is easy. The algorithm works efficiently even in a complex environment, indebted to the generic properties of geographical quadtree modeling for the environment. The usefulness of the algorithm is shown by several simulations.<<ETX>>

Learning control for robot tasks under geometric endpoint constraints

A learning control scheme for a class of robot manipulators whose endpoint is moving under geometrical constraints on a surface is proposed. In this scheme, the input torque command is composed of two different signals updated separately at every trial by different ways. One is updated by the angular velocity error vector which is projected to the tangent plane of the constraint surface in joint space. The other is updated by the magnitude of contact force error at the manipulator endpoint. Not only the uniform boundedness of position and velocity trajectory errors but also the uniform convergence of position and velocity trajectories to their desired ones with repeating practices are proved theoretically. In addition, it is shown that the contact force itself converges to the desired one in the sense of L/sup 2/-norm with repeating practices. Computer simulation results by using a 3 DOF manipulator are presented to demonstrate the effectiveness of the proposed method and to examine the speed of convergence of force trajectories besides position and velocity trajectories. >

A fast path-planning algorithm by synchronizing modification and search of its path graph (mobile robots)

Determination of the shortest collision-free path for a mobile robot between start and goal positions in a workspace is central to the design of an autonomous mobile robot. The authors present a feasible path-planning algorithm which runs on the quadtree representation using a path graph. The quadtree representing the workspace is obtained from fast conversion of a real image taken through a camera on the ceiling. The quadtree integrates both obstacle regions and other regions in the workspace with its hierarchical structure in positioning. By using this hierarchical structure, the mobile robot is reduced to a point and then the forbidden regions where the robot cannot enter into are also understood in the quadtree. Hence, the algorithm can select the shortest collision-free path from the quadtree, i.e. a line between two given positions. Experimental results show that the proposed algorithm is superior to certain conventional algorithms with respect to calculation time.<<ETX>>

A feasible motion-planning algorithm for a mobile robot based on a quadtree representation

A motion-planning algorithm is proposed which fulfils its function fast even if shapes of the robot and its obstacles are complicated. Considering the global obstacle allocation in the robot workspace, the proposed algorithm selects intermediate positions where the mobile robot should pass from a start position to a goal position. Using a systematic motion generation method based on the closest points between the robot and its obstacles, the algorithm generated collision-free robot motions to joint the intermediate positions successively. The algorithm runs on the quadtree representation, obtained from fast conversion of a real image taken through a camera on the ceiling of the workspace. The algorithm can generate collision-free motions while following a change of obstacle allocation. In a comparison with several motion-planning algorithms, it is shown that the proposed algorithm generates fast collision-free robot motions.<<ETX>>

Equivalence relations between learnability, output-dissipativity and strict positive realness

This paper was originally motivated by aiming at explicating why a simple iterative learning control scheme for complicated robot dynamics with strong non-linearities works well in acquiring any given desired motion over a finite or infinite time duration or any periodic motion. To gain a physical insight into the problem, a class of linear dynamical systems with specified input and output of the same dimension is treated by defining two properties: output-dissipativity and learnability. It is then shown that the former implies the latter and furthermore, for a class of linear systems with single input and single output, they are equivalent to each other and each of them is also equivalent to strict positive realness of input-output transfer function. For a class of MIMO (multiple inputs and multiple outputs) systems, it is possible to prove that each of these properties is equivalent to strict positive realness of the input-output transfer function matrix if it is strictly proper or otherwise its direct term from input to output satisfies an extra condtion.