Collinear Mecanum Drive: Modeling, Analysis, Partial Feedback Linearization, and Nonlinear Control

Abstract

The Collinear Mecanum Drive (CMD) is a novel robot locomotion system, capable of generating omnidirectional motion whilst simultaneously dynamically balancing, achieved using a collinear arrangement of three or more Mecanum wheels. The CMD has a significantly thinner ground footprint than existing omnidirectional locomotion methods, which does not need to be enlarged with increasing robot height as to avoid toppling during acceleration or external disturbance. This combination of omnidirectional manoeuvrability and a thin ground footprint allows for the creation of tall robots that are able to navigate through much narrower gaps between obstacles than existing omnidirectional locomotion methods. This allows for greater manoeuvrability in confined and cluttered environments, such as that encountered in the personal service and automated warehousing robotics sectors.This article derives the kinematics and dynamics models of the CMD, analyses controllability and accessibility, and determines the degree to which a CMD can be linearised by feedback. A partial feedback linearisation is then performed, and three practically useful nonlinear controllers are derived using a backstepping design approach, all with convergence and stability guarantees for the fully-coupled nonlinear model. These are demonstrated both in simulation and on a real-world CMD experimental prototype.

MIRRAX: A Reconfigurable Robot for Limited Access Environments

“…The derivation of the kinematic and dynamic model of a reconfigurable mobile robot with Mecanum wheels here extends upon the well established literature on their fixed configuration counterpart [27], [28], [29], [30], [31]. The annotations for the MIRRAX robot are shown in Fig.…”

“…Compared to ballbots [26] which have a single contact point with the ground and are nonholonomic, a straight line configuration with Mecanum wheels has a larger number of contact points and is holonomic. With regards to the controllability of using Mecanum wheels, either arranged in a standard or non-standard shape, this criteria has been evaluated using either the velocity Jacobian [27], [28], linearised dynamics [29], or by heuristics, using a line-crossing approach [30]. The literature in general lacks experimental validation for non-standard configurations; the experiments in [27] evaluated the X-(standard) and Oconfiguration (inverted standard) only.…”

“…The global controllability for a non-linear system, as is the case in this study, does not exist as compared to a linear system. A weaker form of this proof is to instead show that it is small-time locally controllable (STLC), as shown in [29] for a collinear mecanum drive. A similar approach is used here, namely by evaluating the Kalman Controllability Matrix (KCM) using the linearised system dynamics at selected state.…”

“…As the robot approaches the straight-line configuration (φ 1 = −φ 2 = 90°), it becomes dynamically unstable and susceptible to rolling over. Although it was possible to employ controllers capable of both balancing and moving the robot at this configuration [29], the decision was taken to avoid this configuration during operation, except for the ingress and egress from the access port. This was due to the risk of rolling over during operation, which can cause the robot to be unable to right itself as discussed in Section VI-B, and from crashing, which can have detrimental effect on the sensors located on the arm.…”

Set-point Control for a Ground-based Reconfigurable Robot

“…Second, maintaining static balance as the robot's reconfigurability can result in statically unstable configuration i.e. when the wheels are collinear [5], and configurations which result in significant rolling during motion due to the Centre of Mass (CoM) lying close to the support polygon edge. The rolling experienced during motion is undesirable as it can degrade This work was supported by UK Research and Innovation through the Engineering and Physical Science Research Council under grant number EP/P01366X/1 and EP/R026084/1…”