Research objectives and content
In this research project we intend to face the problem of planning feasible paths for the general two-trailer system. It consists of a car pulling two trailers, each hooked at a distance d>0 from the preceding wheel axle. This system can be thought of as composed by two virtual sub-systems: the first one consists of the car and first trailer, while the second one is made of the first and the second trailer. When considered separately, each of these two subsystems is flat. Roughly speaking, a system is flat if we can find a set of outputs (equal in number to the number of inputs) such that all states and inputs can be determined from these outputs without integration. Flat outputs and their derivatives completely describe the trajectories of the relative flat system. For the considered subsystems, this means that their states evolution are characterised by the planar curve described by the flat output, its tangent and its curvature. The key idea that we want to explore is based on the possible decomposition of a non-flat system into flat components. It consist in finding a parameterised family of curves that solve the planning problem for each of the two subsystems and satisfy a constraint imposed by the relation between these two (fictitious) subsystems. Since the real system is controllable, there exist a trajectory of the first trailer such that both the first and the second subsystem are steered to the desired configuration, with the first trailer following this trajectory. The challenge is to find a parameterised family of plane curves, for each subsystem, such that their 'intersection' is not empty.
Training content (objective, benefit and expected Impact)
The requested training would allow the continuation of collaboration between the applicant and the host laboratory that is of primary importance for the continuity of the work and training of the applicant. She is, in fact, realising a preceding project funded by a TMR grant (Contract no. ERB FMBI CT96 1627) started on May the 1st. Preliminary results from this project have been already integrated in a planner experimented at LAAS on the mobile robot Hilare. At the same time, she has enlarged her research interest to the study of the problem that is the subject of the present project. As already mentioned in the current state-of-the-art, an approximating solution to the problem has first been adopted. Besides constituting a possible approach to deepen in the future, it has provided the occasion of analysing the problem of motion planning and control for general car-trailer systems. The requested training would, therefore, provide a mean to complete the started research work as well as the possibility to validate theoretic results on a real system. Links with industry / industrial relevance (22)
The group Robotics and AI at LAAS has close relationship with industry involved in the market of Mobile Robotics or interested in research in this field (Thomson-MidiRobots, Alcatel, Frama-tome, EDF...). The research subject of the applicant lies at the kernel of the mobility function in Mobile Robotics. The objectives of the work are to make the expected results transferable in the framework of these industrial relationships. In view of this objective, it is important to have the possibility to directly experiment control paradigms and planning methods on the real robots available at LAAS.