Perceptive Locomotion through Nonlinear Model Predictive Control

Dynamic locomotion in rough terrain requires accurate foot placement, collision avoidance, and planning of the underactuated dynamics of the system. Reliably optimizing for such motions and interactions in the presence of imperfect and often incomplete perceptive information is challenging. We present a complete perception, planning, and control pipeline, that can optimize motions for all degrees of freedom of the robot in real-time. To mitigate the numerical challenges posed by the terrain a sequence of convex inequality constraints is extracted as local approximations of foothold feasibility and embedded into an online model predictive controller. Steppability classification, plane segmentation, and a signed distance field are precomputed per elevation map to minimize the computational effort during the optimization. A combination of multiple-shooting, real-time iteration, and a filter-based line-search are used to solve the formulated problem reliably and at high rate. We validate the proposed method in scenarios with gaps, slopes, and stepping stones in simulation and experimentally on the ANYmal quadruped platform, resulting in state-of-the-art dynamic climbing.

TAMOLS: Terrain-Aware Motion Optimization for Legged Systems

Terrain geometry is, in general, non-smooth, non-linear, non-convex, and, if perceived through a robot-centric visual unit, appears partially occluded and noisy. This work presents the complete control pipeline capable of handling the aforementioned problems in real-time. We formulate a trajectory optimization problem that jointly optimizes over the base pose and footholds, subject to a heightmap. To avoid converging into undesirable local optima, we deploy a graduated optimization technique. We embed a compact, contact-force free stability criterion that is compatible with the non-flat ground formulation. Direct collocation is used as transcription method, resulting in a non-linear optimization problem that can be solved online in less than ten milliseconds. To increase robustness in the presence of external disturbances, we close the tracking loop with a momentum observer. Our experiments demonstrate stair climbing, walking on stepping stones, and over gaps, utilizing various dynamic gaits.

Elevation Mapping for Locomotion and Navigation using GPU

Perceiving the surrounding environment is crucial for autonomous mobile robots. An elevation map provides a memory-efficient and simple yet powerful geometric representation for ground robots. The robots can use this information for navigation in an unknown environment or perceptive locomotion control over rough terrain. Depending on the application, various post processing steps may be incorporated, such as smoothing, inpainting or plane segmentation. In this work, we present an elevation mapping pipeline leveraging GPU for fast and efficient processing with additional features both for navigation and locomotion. We demonstrated our mapping framework through extensive hardware experiments. Our mapping software was successfully deployed for underground exploration during DARPA Subterranean Challenge and for various experiments of quadrupedal locomotion.

Bipedal Locomotion with Nonlinear Model Predictive Control: Online Gait Generation using Whole-Body Dynamics

The ability to generate dynamic walking in real-time for bipedal robots with compliance and underactuation has the potential to enable locomotion in complex and unstructured environments. Yet, the high-dimensional nature of bipedal robots has limited the use of full-order rigid body dynamics to gaits which are synthesized offline and then tracked online, e.g., via whole-body controllers. In this work we develop an online nonlinear model predictive control approach that leverages the full-order dynamics to realize diverse walking behaviors. Additionally, this approach can be coupled with gaits synthesized offline via a terminal cost that enables a shorter prediction horizon; this makes rapid online re-planning feasible and bridges the gap between online reactive control and offline gait planning. We demonstrate the proposed method on the planar robot AMBER-3M, both in simulation and on hardware.

Adaptive CLF-MPC With Application To Quadrupedal Robots

Modern robotic systems are endowed with superior mobility and mechanical skills that make them suited to be employed in real-world scenarios, where interactions with heavy objects and precise manipulation capabilities are required. For instance, legged robots with high payload capacity can be used in disaster scenarios to remove dangerous material or carry injured people. It is thus essential to develop planning algorithms that can enable complex robots to perform motion and manipulation tasks accurately. In addition, online adaptation mechanisms with respect to new, unknown environments are needed. In this work, we impose that the optimal state-input trajectories generated by Model Predictive Control (MPC) satisfy the Lyapunov function criterion derived in adaptive control for robotic systems. As a result, we combine the stability guarantees provided by Control Lyapunov Functions (CLFs) and the optimality offered by MPC in a unified adaptive framework, yielding an improved performance during the robot's interaction with unknown objects. We validate the proposed approach in simulation and hardware tests on a quadrupedal robot carrying un-modeled payloads and pulling heavy boxes.

Model Predictive Robot-Environment Interaction Control for Mobile Manipulation Tasks

Modern, torque-controlled service robots can regulate contact forces when interacting with their environment. Model Predictive Control (MPC) is a powerful method to solve the underlying control problem, allowing to plan for whole-body motions while including different constraints imposed by the robot dynamics or its environment. However, an accurate model of the robot-environment is needed to achieve a satisfying closed-loop performance. Currently, this necessity undermines the performance and generality of MPC in manipulation tasks. In this work, we combine an MPC-based whole-body controller with two adaptive schemes, derived from online system identification and adaptive control. As a result, we enable a general mobile manipulator to interact with unknown environments, without any need for re-tuning parameters or pre-modeling the interacting objects. In combination with the MPC controller, the two adaptive approaches are validated and benchmarked with a ball-balancing manipulator in door opening and object lifting tasks.

Contact-Implicit Trajectory Optimization for Dynamic Object Manipulation

We present a reformulation of a contact-implicit optimization (CIO) approach that computes optimal trajectories for rigid-body systems in contact-rich settings. A hard-contact model is assumed, and the unilateral constraints are imposed in the form of complementarity conditions. Newton's impact law is adopted for enhanced physical correctness. The optimal control problem is formulated as a multi-staged program through a multiple-shooting scheme. This problem structure is exploited within the FORCES Pro framework to retrieve optimal motion plans, contact sequences and control inputs with increased computational efficiency. We investigate our method on a variety of dynamic object manipulation tasks, performed by a six degrees of freedom robot. The dynamic feasibility of the optimal trajectories, as well as the repeatability and accuracy of the task-satisfaction are verified through simulations and real hardware experiments on one of the manipulation problems.

Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control

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.

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

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 hand-craft 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.

Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions

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.