Addressing Input Saturation and Kinematic Constraints of Overactuated Undercarriages by Predictive Potential Fields Christian P. Connette, Andreas Pott, Martin H¨ agele, Alexander Verl Abstract— Currently, pseudo-omnidirectional, wheeled mo- bile robots with independently steered and driven wheels seem to provide a solid compromise between complexity, flexibility and robustness. Yet, such undercarriages are imposed to the risk of actuator fighting and suffer from singular regions within their configuration space. To address these problems we expand a previously developed potential field (PF) based approach by expanding it with a predictive horizon. The proposed method is based on a model predictive control (MPC) approach, incorporating a gradient descent optimization step via the Pontryagin minimum principle. To enforce adherence to the constraints during optimization, we modify the Lagrange-multipliers within the backpropagation of the costates. The proposed approach is evaluated simulatively w.r.t. the undercarriage of the Care-O- bot R ⃝ 3 mobile robot and is compared to the potential field based and a model predictive control approach. I. I NTRODUCTION Future service robot applications will impose high re- quirements on the employed mobility concepts [1]. Lately, pseudo-omnidirectional, wheeled mobile robots whose un- dercarriage is composed by independently steerable and drivable wheels [2], [3], [4], have emerged as an intermediate term solution. Such systems present a viable compromise between complexity, robustness and flexibility. According to the work by Campion et al. [5], such robots have 3 degrees-of-freedom (DoF). These DoF are split into the degree of steerability   =2, associated to the number of independently steerable wheels, and the degree of mobility   =1, associated to the instantaneously accessible velocity space for the planar motion. Thus, pseudo-omnidirectional mobile robots are able to realize arbitrary velocity and rota- tional commands, however only after reorienting its wheels. Furthermore, this means that such systems are often over- actuated [6]. Therefore, it is important to precisely coordinate all motions to reduce actuator fighting [7], [8]. Moreover, such pseudo-omnidirectional, wheeled mobile robots suffer from singular regions within their configuration space [9], [10], [11]. One possibility to solve this problem [9], [10] is to take into account the singular regions already during trajectory planning and to constrain the accessible velocity space of the robot to a region without singular configurations. Another approach [11] is to avoid singular configurations by treating them as obstacles in a navigation problem and im- plementing a Potential Field (PF) [12], [13] based controller. This work was conducted in the department of Robot Systems at the Fraunhofer Institute for Manufacturing Engineering and Automation (IPA), 70569 Stuttgart, Germany; Contact: phone: +49 711 970 1325; e-mail: christian.connette@ipa.fraunhofer.de Fig. 1. Care-O-bot R ⃝ 3, without coating. To allow quasi-omnidirectional motion the mobile base is composed by four actively steered and driven wheels (www.care-o-bot-research.org). Yet, while successfully applied to various navigation prob- lems [14], [15], [16], PF’s are known for some drawbacks. For instance PF’s are sensitive to local minima. Moreover, when applied to systems changing fast compared to their sample time, PF approaches may lead to local oscillations [17]. Introducing a predictive horizon – according to the methodologies developed within the model predictive control (MPC) domain [18], [19] – promises to remedy the last mentioned problem. While originally focusing on systems with slow dynamics there exists meanwhile a series of works applying MPC approaches to the field of mobile robot navigation. Several works [20], [21], [22] motivated the objective function via repulsive potential fields. Within this work, a potential field approach with a pre- dictive horizon is derived and applied to the control of a pseudo-omnidirectional mobile robot. To address the inter- connected problems of non-holonomic constraints and ac- tuator concurrency control is performed within the spherical representation of the ICM space. To motivate the introduction of a predictive horizon, we draw from the methodologies developed in the MPC domain. Therefore, we start from gradient descent based optimization of the objective function via the Pontryagin minimum principle (PMP) [20], [22]. Then, constraints on the system velocity are enforced by modifying the costates during backpropagation. Therefore, the analogy between Lagrange-multipliers and forces is ex- ploited. Moreover, the calculation of equilibrium velocities, where frictional and attractive forces cancel out each other [12], is expanded to take into account also repulsive forces. The algorithm is evaluated in simulation and compared to the earlier implemented PF- and a MPC-approach. The 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems October 18-22, 2010, Taipei, Taiwan 978-1-4244-6676-4/10/$25.00 ©2010 IEEE 4775