A model-based adaptive controller for robot manipulators under geometric endpoint constraint is proposed on the basis of joint-space orthogonalization of feedback signals. The adaptive law is devised by referring to the basic properties of robot dynamics, which are 1) passivity of robot dynamics, 2) 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 (this is called "joint-space orthogonalization"), and 3) w e 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. In addition, the convergence of force error is proved provided that the endpoint is kept to be in contact with the surface.
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.
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.
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