Whole-Body MPC and Online Gait Sequence Generation for Wheeled-Legged Robots

Abstract

The additional degrees of freedom and missing counterparts in nature make designing locomotion capabilities for wheeled-legged robots more challenging. We propose a whole-body model predictive controller as a single task formulation that simultaneously optimizes wheel and torso motions. Due to the real-time joint velocity and ground reaction force optimization based on a kinodynamic model, our approach accurately captures the real robot's dynamics and automatically discovers complex and dynamic motions cumbersome to handcraft through heuristics. Thanks to the single set of parameters for all behaviors, whole-body optimization makes online gait sequence adaptation possible. Aperiodic gait sequences are automatically found through kinematic leg utilities without the need for predefined contact and lift-off timings. Also, this enables us to reduce the cost of transport of wheeled-legged robots significantly. Our experiments demonstrate highly dynamic motions on a quadrupedal robot with non-steerable wheels in challenging indoor and outdoor environments. Herewith, we verify that a single task formulation is key to reveal the full potential of wheeled-legged robots.

Offline motion libraries and online MPC for advanced mobility skills

“…In our previous work (Bjelonic et al, 2021), we verify that the full set of possible solutions cannot be discovered by such a decomposed method. The individual components do not consider the complete set of physical constraints.…”

“…With the incorporation of online MPC in our article, we finally manage to run these offline trajectories reliably on the robot even in the presence of disturbances and show agile motions on our robot ANYmal. In our previous work (Bjelonic et al, 2021), the MPC only considers future states up to a 1 s time horizon, which leads to unnecessary steps over obstacles. The video in https://youtu.be/_rPvKlvyw2w highlights this issue over stairs and steps.…”

“…More precisely, the MPC in Section 5 models the wheel as a moving point contact. This convention enables us to model conventional point-foot and wheels by merely changing the kinematic constraints (Bjelonic et al, 2021). The elements θ ( t ), p ( t ), ω ( t ), v ( t ) and q j ( t ) of the state vector refer to the orientation of the torso in Euler angles, the position of the torso in world frame W , the angular rate of the COM in torso frame B , the linear velocity of the COM in torso frame B , and the joint positions, respectively.…”

“…Instead, a large amount of pioneering work in model predictive control (MPC) (see reviews by Morari and Lee (1999); Mayne et al (2000); Bertsekas (2005); Diehl et al (2009)) focuses on the online execution of whole-body optimization problems on the real robot in a task-generic fashion (Caron and Pham, 2017; Bjelonic et al, 2021; Bledt and Kim 2019; Bledt et al, 2018; Dantec et al, 2020; Dai et al, 2014; Erez et al, 2013; Farshidian et al, 2017; Grandia et al, 2019a, 2019b; Herdt et al, 2010; Henze et al, 2014; Koenemann et al, 2015; Laurenzi et al, 2018; Mason et al, 2018; Neunert et al, 2018; Paparusso et al, 2020; Zimmermann et al, 2015). Due to fast update rates, MPC finds solutions on the fly while correcting the motion under unforeseen conditions, such as modeling errors and external disturbances, thus offering feedback control.…”

Advanced Skills through Multiple Adversarial Motion Priors in Reinforcement Learning

“…Therefore, we aim to push these robots even more to their limits by executing advanced skills like the quadruped-humanoid transformer in Fig. 1 performed by our wheeled-legged robot [2]. In this work, we rely on a combination of motion priors and RL to achieve such skills.…”