View source for Feasible Trajectories of Linear Dynamic Systems with Inequality Constraints Using Higher-Order Representations

{{HTDB paper
| authors = Sunil K. Agrawal, Nadeem Faiz, Richard M. Murray
| title = Feasible Trajectories of Linear Dynamic Systems with Inequality Constraints Using Higher-Order Representations
| source = 1999 IFAC World Congress
| year = 1998
| type = Conference Paper
| funding = ONR
| url = http://www.cds.caltech.edu/~murray/preprints/afm99-ifac.pdf
| abstract = This paper proposes a method to determine trajectories of dynamic systems that steer
between two end points while satisfying linear inequality constraints arising from limits
on states and inputs. The method exploits the structure of the dynamic system written in a
higher-order form to explicitly eliminate the state equations. The feasible trajectories
of the dynamic system are sought within a characterization with a finite sum of mode
functions. In this paper, the linear inequalities on inputs and states are replaced by a
finite set of linear inequalities on the mode coefficients. This step changes the problem
of trajectory generation into finding a convex polytope enclosed by the linear
inequalities on the mode coefficients. A procedure is then developed to efficiently find
the vertices of this bounding polytope. It is demonstrated in this paper that this method
can generate feasible trajectories of the system in real-time and can quickly update the
trajectories as the terminal conditions are changed. The procedure is demonstrated
numerically by two examples. The results of one of the examples is implemented in hardware
to explore the issues of real-time planning and control. 
| flags = 
| filetype = PDF, 12 pages
| filesize = 2456K
| tag = afm99-ifac
| id = 1998o
}}