3 research outputs found
CIAO: MPC-based Safe Motion Planning in Predictable Dynamic Environments
Robots have been operating in dynamic environments and shared workspaces for
decades. Most optimization based motion planning methods, however, do not
consider the movement of other agents, e.g. humans or other robots, and
therefore do not guarantee collision avoidance in such scenarios. This paper
builds upon the Convex Inner ApprOximation (CIAO) method and proposes a motion
planning algorithm that guarantees collision avoidance in predictable dynamic
environments. Furthermore, it generalizes CIAO's free region concept to
arbitrary norms and proposes a cost function to approximate time optimal motion
planning. The proposed method, CIAO, finds kinodynamically feasible and
collision free trajectories for constrained single body robots using model
predictive control (MPC). It optimizes the motion of one agent and accounts for
the predicted movement of surrounding agents and obstacles. The experimental
evaluation shows that CIAO reaches close to time optimal behavior.Comment: accepted to 21st IFAC World Congres
Time-optimal control with direct collocation and variable discretization
This paper deals with time-optimal control of nonlinear continuous-time
systems based on direct collocation. The underlying discretization grid is
variable in time, as the time intervals are subject to optimization. This
technique differs from approaches that are usually based on a time
transformation. Hermite-Simpson collocation is selected as common
representative in the field of optimal control and trajectory optimization.
Hereby, quadratic splines approximate the system dynamics. Several splines of
different order are suitable for the control parameterization. A comparative
analysis reveals that increasing the degrees of freedom in control, e.g.
quadratic splines, is not suitable for time-optimal control problems due to
constraint violation and inherent oscillations. However, choosing constant or
linear control splines points out to be very effective. A major advantage is
that the implicit solution of the system dynamics is suited for stiff systems
and often requires smaller grid sizes in practice
Stabilizing Quasi-Time-Optimal Nonlinear Model Predictive Control with Variable Discretization
This paper deals with the development and analysis of novel time-optimal
point-to-point model predictive control concepts for nonlinear systems. Recent
approaches in the literature apply a time transformation, however, which do not
maintain recursive feasibility for piecewise constant control parameterization.
The key idea in this paper is to introduce uniform grids with variable
discretization. A shrinking-horizon grid adaptation scheme ensures convergence
to a specific region around the target state and recursive feasibility. The
size of the region is configurable by design parameters. This facilitates the
systematic dual-mode design for quasi-time-optimal control to restore
asymptotic stability and establish a smooth stabilization. Two nonlinear
program formulations with different sparsity patterns are introduced to realize
and implement the underlying optimal control problem. For a class of numerical
integration schemes, even nominal asymptotic stability and true time-optimality
are achieved without dual-mode. A comparative analysis as well as experimental
results demonstrate the effectiveness of the proposed techniques