Obstacle representation by Bump-surfaces for optimal motion-planning

Rapid motion planning algorithm for optimal UVMS interventions in semi-structured environments using GPUs

“…The algorithm maps the workspace onto a Bump-surface entity [21], that is constantly updated based on the sensor readings. The method could be used to generate a near optimum, valid motion plan into a semi-structured or un-known environment.…”

“…The actual model of the UVMS is being considered, while the environment is rapidly mapped onto a Bump-surface entity [21] for fast collision detection by implementing a parallel algorithm that runs on a GPU. The computationally expensive transformation of the obstacles onto the configuration space is avoided since the collision checking is performed on the Bump-surface.…”

“…In this paper, a Bump-surface embedded to a 4-D Euclidean space is used to check for an obstacle free motion plan. The Bump-surface concept for motion planning was introduced in [21] and later extended to a mobile manipulator in a 3-D environment [24]. The construction of the Bump-surface relies on a three dimensional grid of control points with length (L) on each dimension a step (d), depending on the desired motion planning accuracy.…”

“…The construction of the Bump-surface relies on a three dimensional grid of control points with length (L) on each dimension a step (d), depending on the desired motion planning accuracy. The value of the fourth dimension of every control point is given by a modified z-value algorithm (described in [21]), depending whether the point lies inside an obstacle or not. The modified z-value algorithm procedure is described in detail in Section 3.…”

Motion planning for multiple non-holonomic robots: a geometric approach

“…26 This algorithm considers that W is discretized into uniform subintervals along its u, v, and t orthogonal directions, respectively, forming a grid of points where p, f , and g denote the degree in the u, v, and t direction of the B-Spline surface respectively. p ij k are the grid points, and N i,p (u), N j,f (v), and N k,g (t) are the basis functions.…”