Optimal Control of Nonholonomic and Underactuated Systems

Modeling, analysis, control, and experimental validation in mobile robotics

 

 

Fig. 1: Custom-built non-holonomic vehicles used at the institute
Fig. 1: Custom-built non-holonomic vehicles used at the institute

Project Description

Nonholonomic systems are ubiquitous in mobile robotics, logistics, transportation, and everyday life. Well-known examples of such systems are differential-drive (service) robots, vehicles with trailers, or cars. These systems all have in common that, instantaneously, they cannot move in all directions along the state-space manifold on which their motions evolve due to the presence of nonholonomic constraints. As one consequence, this key property results in a lack of controllability of the systems' linearization and renders system analysis, motion planning, and control design significantly more sophisticated. Although it has been known for decades that deriving a controller is challenging for this system class, bridging the gap to the underlying geometry has been a matter of more recent research. Indeed, to obtain an expressive distance measure, e.g., when thinking of the vehicle's distance to a goal point, one needs to think in terms of sub-Riemannian instead of Euclidean geometry. This is also a descriptive explanation of why, in model predictive control settings, the conventional choice of quadratic costs, related to squared Euclidean errors, does not reliably drive vehicles to desired setpoints.

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Vid. 1: Visualization of the non-quadratic stage costs’ level sets to precisely control a differential-drive mobile robot.

This geometric perspective is also embodied in the design of a functioning model predictive controller by utilizing tailored non-quadratic costs. Following a general design procedure for kinematically modeled nonholonomic systems, nonholonomic vehicles can be precisely driven to their desired setpoint, see Vid. 2, where exemplarily a robot-trailer system is controlled. Notably, this generic approach can also be employed to derive tailored (distributed) controllers for swarms of nonholononmic mobile robots and for heterogeneous robotic swarms in general.

Current research questions include the further investigation of the role of sub-Riemannian geometry in the context of model predictive control and extending recent theoretically sound findings to the broader class of underactuated robotic systems.

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Vid. 2: Parallel parking of a non-holonomic mobile robot with an attached trailer.

This image shows Henrik Ebel

Henrik Ebel

Dr.-Ing.

(2016 - 2024)

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