Coordinated dual-arm manipulation tasks can be broadly characterized as possessing absolute and relative motion components. Relative motion tasks, in particular, are inherently redundant in the way they can be distributed between end-effectors. In this work, we analyse cooperative manipulation in terms of the asymmetric resolution of relative motion tasks. We discuss how existing approaches enable the asymmetric execution of a relative motion task, and show how an asymmetric relative motion space can be defined. We leverage this result to propose an extended relative Jacobian to model the cooperative system, which allows a user to set a concrete degree of asymmetry in the task execution. This is achieved without the need for prescribing an absolute motion target. Instead, the absolute motion remains available as a functional redundancy to the system. We illustrate the properties of our proposed Jacobian through numerical simulations of a novel differential Inverse Kinematics algorithm.
Relative Jacobian methods model solely the relative motion task @cite_34 @cite_25 @cite_29 , making it a common choice when addressing tasks that require just the relative motion space, such as machining @cite_2 @cite_33 @cite_14 , assembly @cite_18 or drawing @cite_15 . The absolute motion is part of the relative Jacobian's redundant space. This can be exploited, e.g., to enhance self-collision and obstacle avoidance as secondary tasks @cite_22 , or for joint-limit avoidance @cite_16 @cite_7 @cite_0 .
@cite_18 @cite_14 @cite_33 @cite_22 @cite_7 @cite_29 @cite_16 @cite_0 @cite_2 @cite_15 @cite_34 @cite_25
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A formulation for online trajectory generation for two robots cooperating to perform an assembly task is derived. The two robots are treated as a single redundant system. A Jacobian is formulated that relates the joint rates of the entire system to the relative motion of one of the hands with respect to the other. The minimum norm solution of this relative Jacobian equation results in a set of joint rates which perform the cooperative task. In addition to the cooperative task, secondary goals, which include obstacle and joint limit avoidance, are specified using velocities in the null space of the relative Jacobian. This formulation also allows the robots to be controlled in parallel on independent tasks This paper presents an alternative to the Potential Field Method of computing local collision-free motions for general manipulators. The main distinction is that we separate the description of the task from constraints of anti-collision. This enables to control accurately all relevant measures of the problem. A task is expressed by the minimization of a function plus eventually some geometric constraints, whereas anti-collision is translated into very simple linear constraints through the methods of the velocity dampers and the tangent separating planes. This approach is applied to the control of manipulators with a high number of degrees of freedom, using hierarchical descriptions of the environment and the robots. This is illustrated by two realizations, path planning for a ten link manipulator in the cluttered environment of a nuclear plant reactor, and cooperative tasks between two six degree of freedom robots. In the end we discuss how to incorporate the action of a global planner in this general framework. We present an approach to control a 6-degree-of-freedom (DOF) manipulator using an uncalibrated visual servoing (VS) approach that addresses the challenges of choosing proper image features for target objects and designing a VS controller to enhance the tracking performance. The main contribution of this paper is the definition of a new virtual visual space (image space). A novel stereo camera model employing virtual orthogonal cameras is used to map 6-D poses from Cartesian space to this virtual visual space . Each component of the 6-D pose vector defined in this virtual visual space is linearly independent, leading to a full-rank @math image Jacobian matrix , which allows avoiding classical problems, such as image space singularities and local minima. Furthermore, the control for rotational and translational motion of robot is decoupled due to the diagonal image Jacobian. Finally, simulation results with an eye-to-hand robotic system confirm the improvement in controller stability and motion performance with respect to conventional VS approaches. Experimental results on a 6-DOF industrial robot are provided to illustrate the effectiveness of the proposed method and the feasibility of using this method in practical scenarios. We explore global randomized joint space path planning for articulated robots that are subject to task space constraints. This paper describes a representation of constrained motion for joint space planners and develops two simple and efficient methods for constrained sampling of joint configurations: Tangent Space Sampling (TS) and First-Order Retraction (FR). Constrained joint space planning is important for many real world problems involving redundant manipulators. On the one hand, tasks are designated in work space coordinates: rotating doors about fixed axes, sliding drawers along fixed trajectories or holding objects level during transport. On the other, joint space planning gives alternative paths that use redundant degrees of freedom to avoid obstacles or satisfy additional goals while performing a task. In simulation, we demonstrate that our methods are faster and significantly more invariant to problem algorithm parameters than existing techniques.