Obstacle-free Workspace Research Articles

The planning of optimal motions of non-holonomic systems

A new method to the planning of optimal motions of the non-holonomic systems is presented. It is based on a non-classical formulation of the Pontryagin Maximum Principle given in variational form, which handles efficiently various control and/or state-dependent constraints. They arise naturally due to both physical limits of the actuators of the non-holonomic systems and potential existence of obstacles in the workspace. The method proposed here provides continuous solutions in infinite-dimensional control space. It seems to be in contrast to majority of known optimization algorithms which project infinite-dimensional control space into finite-dimensional one and then apply techniques of linear and/or nonlinear programming, thus resulting only in near-optimal trajectories. Moreover, the offered control schemes do not require computation of inverse or pseudo-inverse of the Jacobian in the case of classic non-holonomic motion planning what also results in numerical stability of our approach. The performance of the proposed control strategies is illustrated through computer simulations for a chosen class of non-holonomic structures operating in both an obstacle-free workspace and a workspace including obstacles. Numerical comparison of our control scheme with the representative algorithms known from the literature is also given.

Collision-free workspace of parallel mechanisms based on an interval analysis approach

SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

A new automatic motion planning algorithm for a 4-degree-of-freedom parallel kinematic manipulator based on the centre sphere method

This study investigates a new automatic motion planning algorithm for industrial robots performing a pick-and-place task in an obstacle-free workspace. The new technique finds an optimal trajectory for a parallel kinematic manipulator. The centre sphere method and multi-objective optimisation are used to solve this problem. To obtain an optimal path, an objective function that includes a hypothetical jerk fitness value, a path length function and a virtual obstacle avoidance function is defined, and the path planning problem is solved using particle swarm optimisation. For greater efficiency, the planning problem is modified to include physical constraints on the robot. The method is tested on a 4-degree-of-freedom parallel kinematic manipulator through simulations, where the optimum virtual sphere radius is obtained. Experiments are performed with an actual parallel kinematic manipulator, and a comparison of the performance of the robot executing the same tasks with trajectories obtained using the new method and two existing methods is made. The results show the efficiency and the effectiveness of the proposed approach in determining the optimal trajectory for a 4-degree-of-freedom parallel kinematic manipulator in an obstacle-free workspace.

An Innovative Motion Planning for 4-DOF PKM

This paper presents an innovative motion planning algorithm for pick and place operations in the industry. The new technique is to seek optimal dynamics pattern for PKM(parallel kinematic manipulator), this is achieved by two parts: First, to achieve optimal path planning, a center sphere method based on virtual obstacle path planning method is proposed to solve such path planning with Particle Swarm Optimization (PSO); Second, to enhance the efficiency of the robot, time optimal trajectory planning is finished with respect to robotic physical constraints. Then, the method applied to a 4-DOF PKM is tested by numerical simulations, some examples are presented making comparisons on same tasks assigned by different sphere radius, the simulation results show the efficiency and the effectiveness of the proposed approach to determine the optimal motion pattern for 4-DOF PKM in obstacle-free workspace.

Path Following by the End-Effector of a Redundant Manipulator Operating in a Dynamic Environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.

A Framework for Real-time Path Planning in Changing Environments

We present a new method for generating collision-free paths for robots operating in changing environments. Our approach is closely related to recent probabilistic roadmap approaches. These planners use preprocessing and query stages, and are aimed at planning many times in the same environment. In contrast, our preprocessing stage creates a representation of the configuration space that can be easily modified in real time to account for changes in the environment, thus facilitating real-time planning. As with previous approaches, we begin by constructing a graph that represents a roadmap in the configuration space, but we do not construct this graph for a specific workspace. Instead, we construct the graph for an obstacle-free workspace, and encode the mapping from workspace cells to nodes and arcs in the graph. When the environment changes, this mapping is used to make the appropriate modifications to the graph, and plans can be generated by searching the modified graph. In this paper, we first discuss the construction of the roadmap, including how random samples of the configuration space are generated using an importance sampling approach and how these samples are connected to form the roadmap. We then discuss the mapping from the workspace to the configuration space roadmap, explaining how the mapping is generated and how it can be encoded efficiently using compression schemes that exploit redundancy in the mapping. We then introduce quantitative robustness measures and show how these can be used to enhance the robustness of the roadmap to changes in the environment. Finally, we evaluate an implementation of our approach for serial-link manipulators with up to 20 joints.

A Framework for Real-time Path Planning in Changing Environments

We present a new method for generating collision-free paths for robots operating in changing environments. Our approach is closely related to recent probabilistic roadmap approaches. These planners use preprocessing and query stages, and are aimed at planning many times in the same environment. In contrast, our preprocessing stage creates a representation of the configuration space that can be easily modified in real time to account for changes in the environment, thus facilitating real-time planning. As with previous approaches, we begin by constructing a graph that represents a roadmap in the configuration space, but we do not construct this graph for a specific workspace. Instead, we construct the graph for an obstacle-free workspace, and encode the mapping from workspace cells to nodes and arcs in the graph. When the environment changes, this mapping is used to make the appropriate modifications to the graph, and plans can be generated by searching the modified graph. In this paper, we first discuss the construction of the roadmap, including how random samples of the configuration space are generated using an importance sampling approach and how these samples are connected to form the roadmap. We then discuss the mapping from the workspace to the configuration space roadmap, explaining how the mapping is generated and how it can be encoded efficiently using compression schemes that exploit redundancy in the mapping. We then introduce quantitative robustness measures and show how these can be used to enhance the robustness of the roadmap to changes in the environment. Finally, we evaluate an implementation of our approach for serial-link manipulators with up to 20 joints.