Virtual reality can be a very useful tool for complicated programming, planning, controlling and teleoperating robots. As yet the application of virtual reality to cooperation and conflict resolution between multiple robots has received little attention. In the paper, an event-driven virtual reality system for two robots is proposed and implemented. This system uses a standard VR package to implement the environment, thus allowing easier development of tasks, skills and behaviours. The assemblies in the virtual scene, i.e. CAD counterparts of these two robots, act like an outer protective skin to events from the variable environment around them such as collisions. Thus the corresponding safety actions can then be taken. The virtual and real environments are physically connected through a LAN using the TCP/IP protocol. Once the virtual assemblies are placed in safe and desirable goal locations, the real links update their locations using recorded trajectory points through path planning and collision avoidance. This approach prevents the VR from causing collisions between two real links, and between the real links and their environment. This system has provided a useful extension to current virtual reality systems for single robots. Also this system has application potential in multiple robot teleoperation tasks.

This work describes a path planning method applied to a three robot system. Trajectories are optimized to allow minimum time performance of the overall system. Mathematical programming methods with a global approach are used.

Moving the individual components of a chain in response to forces and torques on any of its links is a difficult problem to solve for real-time applications, e.g. for a virtual reality application. Here, an original method using dynamics is proposed to move the individual parts of chain mechanisms which are resident in a virtual reality environment. The computation of this method is straightforward, and uses a new formulation suited to virtual reality to build the dynamic model. With this approach neither the kinematic nor the inverse kinematic models are needed. Simulations of a five link planar closed system and of a three DOF parallel robot are used to demonstrate the method. An interface method which enables both the position and the orientation of the held link to be altered is also described.

Where two robot arms hold a common object and their usable space is limited such as inside an automatic instrument it is important to determine its maximum extreme distance or reachable workspace. Obviously, the grasping orientations and placement of the two arms are crucial to maximising the distance and workspace. To date, these factors have been ignored. This problem is much more difficult than that for a single arm and many methods for a single arm are no longer applicable, due to many extra constraints, variables and joint configurations. Here, a new approach to this problem is proposed. The problem is formulated as a multivariable nonlinear constrained optimisation problem and it is solved using sequential quadratic programming (SQP). With this method, the optimal grasping with optimal placement of the two arms, the extreme joint configurations and the maximum extreme distance can be obtained The computational results show that the distance takes its maximum where a small number of joint configurations are at their singularities, which is quite different from the situations of a single arm and from intuition. This method is illustrated using an example, where a rod is held by the two-finger grippers of two SCARA-type robot arms. Objects of different shapes, such as a plate, can be treated as special cases of the rod.

The objective of inspection task sequence planning for two robot arms is not only to find a series of common optimal final configurations, but to find a time-optimal task sequence of inspection points. The time-suboptimal final configurations are solved using a (continuous) nonlinear optimization method. The task sequence planning is formulated as a variation of the travelling salesman problem (an integer optimization) and is solved by simulated annealing. The time-suboptimal task sequence planning and time-efficient trajectory planning are integrated and the related computational problems are addressed and solved. The proposed method is applied to an environment containing two cooperative SCARA type inspection robot arms. Computations have been carried out for 4-20 moving points/cities in a route where both arms move. This is compared with completing the task with the same goal points in a route where only one arm moves. The conclusion is that it is much more efficient if two robot arms work in cooperative mode. Experiments have also been conducted on an experimental system, this gave satisfactory results which are consistent with those obtained by simulation.

Planning for effective manipulation of single, redundant or multiple robot systems requires the consideration of the DOF, dexterity, tasks and constraints. A new approach to redundancy resolution for multiple cooperative robots is proposed. A relative Jacobian, thus relative dexterity, is clearly defined and derived for multiple robots. Sequential quadratic programming (SQP) is used to optimize the relative dexterity of the robots whilst satisfying task requirements and limits on joint angles. With this approach it is not necessary to balance the weightings between the performance index and those constraint terms in the cost function. Further the resulting joint configurations are globally optimal with respect to the specified cost. An illustrative example is included to demonstrate the usefulness of this approach. From this example, the relative dexterity of the arms has been found to be more useful than individual arm dexterities in planning the cooperative task.

In an order to remove the disadvantages of classical formulations for geometric and dynamic models (especially for closed chain systems), a simple and efficient parametrization is developed. This parametrization is well adapted to virtual reality visualisation (geometric applications), because of the linearity of the geometric model. The method allows the calculation of the configuration of the links without having to generate complicated geometrical models using homogeneous transformations. A simulation on a five link planar closed system has been efficiently carried out. Further extensions of the work are described.

A practical approach to time-efficient trajectory planning for two cooperative industrial robots with free final configurations is presented. A time-efficient trajectory planning problem is then formulated which uses time-efficient acceleration profiles and is subject to limits on joint positions, velocities, accelerations and jerks. The formula is further simplified by suitably choosing the time intervals of the profile. The optimization problem is solved using a nonlinear optimization method, sequential quadratic programming (SQP). The computation problem arising thereby is successfully dealt with. The proposed method is applied to an environment containing two RTX SCARA type robot arms where their final configurations are relatively given with respect to each other, e.g. in a tool/workpiece operation, and are free with respect to the world frame. The problem is solved in almost real-time. For each robot arm, at least one of the resulting joint trajectories reaches its limit velocity. These joint trajectories are used as reference inputs to a robot control system for the two RTX arms realised on a transputer network. Experiments demonstrating feasibility of this method are conducted.

In this paper time-optimal, smooth and collision-free cubic spline path planning in an environment with two industrial robot arms is implemented. A suitable objective function combining the requirements of time optimality and smoothness of paths is put forward which is subject to the continuity of joint positions, velocities, and accelerations, the limits on their rates of change and collision-free constraints. A fast and effective collision detection method is used. A nonlinear optimization method is used to solve this problem. The resulting joint trajectories or spatial Cartesian paths are time-optimal, smooth and collision-free. The feasibility of this method is illustrated both by simulation and by experimental results with two RTX SCARA type robot arms. Further fast parallel implementation is outlined.

In this paper a new approach to time-optimal and smooth constrained path (continuous path) planning for robot manipulators is presented. A suitable objective function to combine time-optimal and smooth trajectory planning is found. The optimization process involves first obtaining smooth and time-suboptimal joint paths by minimizing the objective function, and then contracting travelling time by scaling the resulting time intervals for time-optimal joint paths so that the resulting velocities or accelerations or joints at some knots of die paths are maximal within their limitations. The resulting joint paths are smooth, time-optimal with optimal velocity profiles and therefore suitable for robotic motion. The feasibility of this method is illustrated by simulation and experimental results with an RTX SCARA type robot.>