### Optimization and Systems Theory Seminar

Friday, May 23, 2003, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Petter Ögren**

Division of Optimization and Systems Theory

Department of Mathematics

KTH

E-mail: petter@math.kth.se

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Formation and obstacle avoidance in mobile robot control

This talk gives an overview of my thesis. The thesis consists of four
independent papers concerning the control of mobile robots in the
context of obstacle avoidance and formation keeping.
The first paper describes a new theoretically verifiable approach to
obstacle avoidance. It merges the ideas of two previous methods, with
complementary properties, using a combined control Lyapunov function
(CLF) and model predictive control (MPC) framework.

The second paper investigates the problem of moving a fixed formation
of vehicles through a partially known environment with obstacles.
Using an input to state (ISS) formulation the concept of configuration
space obstacles is generalized to leader follower formations. This
generalization then makes it possible to convert the problem into a
standard single vehicle obstacle avoidance problem, such as the one
considered in the first paper. The properties of goal convergence and
safety thus carries over to the formation obstacle avoidance case.

In the third paper, coordination along trajectories of a nonhomogenuos
set of vehicles is considered. Using a control Lyapunov function
approach, properties such as bounded formation error and finite
completion time is shown.

Finally, the fourth paper applies a generalized version of the control
in the third paper to translate, rotate and expand a formation. It is
furthermore shown how a partial decoupling of formation keeping and
formation mission can be achieved. The approach is then applied to a
scenario of underwater vehicles climbing gradients in search for
specific thermal/biological regions of interest. The sensor data
fusion problem for different formation configurations is investigated
and an optimal formation geometry is proposed.

Calendar of seminars

*Last update: May 15, 2003 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*