DOI: 10.18419/darus-5706
title: Experiment Videos on Setpoint Stabilization of Nonholonomic Mobile Robots and Their Formations Using Geometry-Conforming Model Predictive Control

description: &lt;p&gt;The provided videos document experimental results on setpoint stabilization of various wheeled mobile robots and their formations using tailored model predictive control (MPC) schemes. The controllers are formulated at the kinematic level, i.e., they employ kinematic models of the robots to predict their future behavior and use the robots' velocities as control inputs. The resulting velocity commands are then executed by onboard low-level velocity controllers running at 100 Hz. Three different robot kinematics are considered: a differential-drive robot, the same kinematics with an attached trailer, and a rear-wheel-driven car-like robot. In addition to single-robot control, the stabilization of differential-drive robot formations is also demonstrated using a distributed realization of the proposed geometry-conforming model predictive controllers. For each case, two MPC variants without additional stabilizing constraints or costs are implemented and experimentally evaluated. First, MPC schemes employing tailored, geometry-conforming stage costs are used. The resulting closed-loop trajectories of the robot positions are shown as orange lines in the videos, while the desired setpoints are indicated by red crosses. Second, for comparison, MPC schemes based on conventional quadratic stage costs are implemented, with all other controller parameters kept identical. The corresponding closed-loop trajectories are shown as solid green lines in the videos. For the considered formation control scenarios, the formation mean is additionally highlighted by a dashed violet line. For more details on the implementation of the controllers and the actual parameters used, please refer to the related publication.&lt;/p&gt;

&lt;p&gt;The experiments demonstrate that only the controllers employing the tailored geometry-conforming stage costs are able to reliably steer the robots to the desired setpoints with high accuracy. This finding also holds for the formation control of multiple differential-drive robots. In contrast, controllers based on conventional quadratic stage costs fail to achieve reliable setpoint stabilization. This is a direct consequence of the underlying nonholonomic geometry of the considered wheeled mobile robots, which is not adequately captured by quadratic stage costs. At a high level, interpreting the state-dependent part of the stage cost as a distance measure to the desired setpoint highlights the inherent problem of conventional quadratic stage costs. For nonholonomic systems, the distance between two configurations cannot be represented by the Euclidean distance in the state space, not even locally.&lt;br&gt;
Instead, meaningful distances must be measured along feasible paths that respect the nonholonomic constraints. To account for this, concepts from sub-Riemannian geometry are incorporated into the design of the geometry-conforming stage costs, resulting in cost functions with mixed exponents. Intuitively, directions that are harder to control are penalized more strongly close to the desired setpoint than directions that are easier to control.&lt;/p&gt;

The naming of the videos follows the appearance in the related publication.
Note that, while trajectories corresponding to quadratic stage cost controllers are shown as dashed green lines in the related publication for visual clarity, they are displayed as solid green lines in the provided videos. In addition to the standard Cartesian coordinate formulation, supplementary videos are provided in which the controllers for the differential-drive robot are based on a polar coordinate representation, both for the single-robot control task and for the formation control scenario. This way, the single-robot robot and the formation locally approach their desired setpoints along circular arcs rather than straight-line paths.