EURON - Novel methods for Motion Planning (2004-2006)

BUMP-SURFACES FOR OPTIMAL MOTION PLANNING [1] [2]

 

 

BUMP-SURFACE

  • Represents entire 2D robot environment via tensor product B-Spline Surface.
  • The path is represented by a B-Spline onto the Bump-Surface.
  • Takes full advantage of these mathematical entities, especially control points.
  • The final motion planning problem is formulated as a global optimization problem, solved using combination of Genetic Algorithms and Conjugate Gradient methods [1].

Solution_Bump_Surf

Fig. A1 - 2D environment with non-convex obstacle and robot’s optimal path.

Bump_Surface

Fig. A2 - The corresponding Bump-Surface.

BUMP-HYPER SURFACE

  • Extension of the Bump-Surface from 2D to 3D Euclidean space.

Scene_1

Fig. A3 – A 3D environment with polyhedral obstacles (pyramids) and determined optimal path. The path is defined by four control points: the start-point, two points at the space in-between and the end-point.

Scene_2

Fig. A4 – A 3D environment with polyhedral obstacles and the optimal path. The determined path is defined by means of six control points, all located in space

Scene_3

Fig. A5 - A 3D environment with a torus obstacle, where the start point is at the torus centre. The required path is defined by three control points: The start point, a middle point  and the end point.

CONCLUSIONS

 

  • Computational time does not depend on the number of obstacles but on the size of the control parameters of the GAs and density of grid points [2].
  • The accuracy of the solution depends on the density of the grid points.
  • An optimal path can be found even in significantly complicated environments, cluttered with obstacles of arbitrary size and location.
  • The final path is always smooth and conformal to the objectives, so the robot can follow it avoiding jerky motions.

MULTI-AGENT BASED MANIPULATOR CONTROL

AND MOVING OBSTACLE AVOIDANCE [3]

 

KINEMATIC MODEL

 

  • Planar and 3D manipulators.
  • With any serial combination of rotational and translational joints.
  • Manipulator base may be fixed or may move freely or on predefined path.

 

CONCEPTUAL MODEL

 

  • Potentially expandable rods (length Li in [Li-min, Li-max]).
  • Rods connected at their endpoints using pins (angle Ai in [Ai-min, Ai-max]).
  • Forming a chain that behaves like a rope (given high number of rods & pins).

ARK_PhysicalConceptual

Fig. B1 – conceptual model maintaining a 1-1 mapping with the kinematic model and its constraints.

CHANGE EVENT PROPAGATION

  • Any chain part (not only the tool tip) can initiate motion, via commands of planner module or human operator: chain is split by mover in two sub-chains.
  • A slave has its own slave (master-slave hierarchy, nested relationships).
  • Each slave tries to react and adapt to its master’s state change event [3].

ARK_EventsExceptions

Fig. B2 - State change events at the head of each sub-chain propagate towards its tail.

REACTION TO MASTER’S STATE CHANGE EVENTS

 

ARK_Push

ARK_PushResizePull_final

ARK_Pull

Fig. B3 - Two basic constraint preservation behaviors: Push & Pull. Slave moves on guiding line.

REACTION TO SENSED OBSTACLES

        

ARK_PushRotate

 

ARK_PullRotate

Fig. B4 - Guiding line for slave motion rotates around master pin, to avoid “contact” with obstacle.

REFERENCES

 

  1. P.N. Azariadis, N.A. Aspragathos, "Obstacle Representation by Bump-Surfaces for Optimal Path-Planning", Journal of Robotics and Autonomous Systems (accepted for publication).
  2. E. Xydias, N.A. Aspragathos (2004), "Bump-Hyper Surfaces For Optimal Motion Planning in Three Dimensional Spaces", RAAD 04, Brno, 2-5 June 2004.
  3. G.I. Birbilis, N.A. Aspragathos (2004), “Multi-Agent Manipulator Control and Moving Obstacle Avoidance”, ARK 04, Sestri Levante, Italy, 28 June – 1 July 2004.