The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highlycompliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance.

Autonomous mobile manipulation offers a dual advantage of mobility provided by a mobile platform and dexterity afforded by the manipulator. In this paper, we present a wholebody optimal control framework to jointly solve the problems of manipulation, balancing and interaction as one optimization problem for an inherently unstable robot. The optimization is performed using a Model Predictive Control (MPC) approach; the optimal control problem is transcribed at the end-effector space, treating the position and orientation tasks in the MPC planner, and skillfully planning for end-effector contact forces. The proposed formulation evaluates how the control decisions aimed at end-effector tracking and environment interaction will affect the balance of the system in the future. We showcase the advantages of the proposed MPC approach on the example of a ball-balancing robot with a robotic manipulator and validate our controller in hardware experiments for tasks such as end-effector pose tracking and door opening.

The regular inspection of sewer systems is essential to assess the level of degradation and to plan maintenance work. Currently, human inspectors must walk through sewers and use their sense of touch to inspect the roughness of the floor and check for cracks. The sense of touch is used since the floor is often covered by (waste) water and biofilm, which renders visual inspection very challenging. In this paper, we demonstrate a robotic inspection system which evaluates concrete deterioration using tactile interaction. We deployed the quadruped robot ANYmal in the sewers of Zurich and commanded it using shared autonomy for several such missions. The inspection itself is realized via a well-defined scratching motion using one of the limbs on the sewer floor. Inertial and force/torque sensors embedded within specially designed feet captured the resulting vibrations. A pretrained support vector machine (SVM) is evaluated to assess the state of the concrete. The results of the classification are then displayed in a three-dimensional map recorded by the robot for easy visualization and assessment. To train the SVM we recorded 625 samples with ground truth labels provided by professional sewer inspectors. We make this data set publicly available. We achieved deterioration level estimates within three classes of more than 92% accuracy. During the four deployment missions, we covered a total distance of 300 m and acquired 130 inspection samples.

No abstract

The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.

Abstract-In this paper, we present an algorithm for planning and control of legged robot locomotion. Given the desired contact sequence, this method generates gaits and dynamic motions for legged robots without resorting to simplified stability criteria. The method uses direct collocation for searching for solutions within the constraint-consistent subspace defined by the robot's contact configuration. For the differential equation constraints of the collocation algorithm, we use the so-called direct dynamics of a constrained multibody system. The dynamics of a legged robot is different for each contact configuration. Our method deals with such a hybrid nature, and it allows for velocity discontinuities when contacts are made. We introduce the projected impact dynamics constraint to enforce consistency during mode switching. We stabilize the plan using an inverse dynamics controller compatible with the optimal feed-forward control of the motion plan. As a whole, this approach reduces the complexity associated with specifying dynamic motions of a floating-base robot under the constant influence of contact forces. We apply this method on a hydraulically-actuated quadruped robot. We show two types of gaits (walking and trotting) as well as diverse jumping motions (forward, sideways, turning) on the real system. The results presented here are one of the few examples of an optimal control problem solved and satisfactorily transferred to a real torquecontrolled legged robot.

The problem of dynamic locomotion over rough terrain requires both accurate foot placement together with an emphasis on dynamic stability. Existing approaches to this problem prioritize immediate safe foot placement over longer term dynamic stability considerations, or relegate the coordination of foot placement and dynamic stability to heuristic methods. We propose a multi-layered locomotion framework that unifies Control Barrier Functions (CBFs) with Model Predictive Control (MPC) to simultaneously achieve safe foot placement and dynamic stability. Our approach incorporates CBF based safety constraints both in a low frequency kino-dynamic MPC formulation and a high frequency inverse dynamics tracking controller. This ensures that safety-critical execution is considered when optimizing locomotion over a longer horizon. We validate the proposed method in a 3D stepping-stone scenario in simulation and experimentally on the ANYmal quadruped platform.