Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and derivatives-free search to plan both foothold locations and horizontal motions due to the local minima produced by the terrain model. It jointly optimizes body motion, step duration and foothold selection, and it models the terrain as a cost-map. Due to the novel attitude planning method, the horizontal motion plans can be applied to various terrain conditions. The attitude planner ensures the robot stability by imposing limits to the angular acceleration. Our whole-body controller tracks compliantly trunk motions while avoiding slippage, as well as kinematic and torque limits. Despite the use of a simplified model, which is restricted to flat terrain, our approach shows remarkable capability to deal with a wide range of non-coplanar terrains. The results are validated by experimental trials and comparative evaluations in a series of terrains of progressively increasing complexity.
This paper systematically decomposes a quadrupedal robot into bipeds to rapidly generate walking gaits and then recomposes these gaits to obtain quadrupedal locomotion. We begin by decomposing the full-order, nonlinear and hybrid dynamics of a three-dimensional quadrupedal robot, including its continuous and discrete dynamics, into two bipedal systems that are subject to external forces. Using the hybrid zero dynamics (HZD) framework, gaits for these bipedal robots can be rapidly generated (on the order of seconds) along with corresponding controllers. The decomposition is achieved in such a w…
Politecnico di Milano（米兰理工大学）；Istituto Italiano di Tecnologia（意大利技术研究院）
Hybrid wheeled-legged locomotion is a navigation paradigm only recently opened up by novel robotic designs,e.g. the centaur-type humanoid CENTAURO [1] or the quadruped ANYmal [2] in its configuration featuring non-steerable wheels. The term Hybrid Locomotion is hereafter used to indicate a particular type of locomotion, achieved with simultaneous and coordinate use of legs and wheels,see Fig. 1. Such choice stems at the intersection between legged locomotion and the simpler wheeled navigation, in order to get the best from both techniques: agility and ability to traverse uneven terrains from t…
Robotic Systems Lab, ETH Zurich（苏黎世联邦理工学院机器人系统实验室）；Robotics and Artificial Intelligence Lab, KAIST（韩国科学技术院机器人与人工智能实验室）；Intelligent Systems Lab, Intel（英特尔智能系统实验室）
Some of the most challenging environments on our planet are accessible to quadrupedal animals but remain out of reach for autonomous machines. Legged locomotion can dramatically expand the operational domains of robotics. However, conventional controllers for legged locomotion are based on elaborate state machines that explicitly trigger the execution of motion primitives and reflexes. These designs have escalated in complexity while falling short of the generality and robustness of animal locomotion. Here we present a radically robust controller for legged locomotion in challenging natural en…
Dynamic Quadrupedal Legged and Aerial Locomotion via Structure Repurposing
Department of Electrical and Computer Engineering, Northeastern University（电气与计算机工程系，东北大学）；Department of Aerospace Engineering, California Institute of Technology（航空航天工程系，加州理工学院）
We present a versatile nonlinear model predictive control (NMPC) formulation for quadrupedal locomotion. Our formulation jointly optimizes a base trajectory and a set of footholds over a finite time horizon based on simplified dynamics models. We leverage second-order sensitivity analysis and a sparse Gauss-Newton (SGN) method to solve the resulting optimal control problems. We further describe our ongoing effort to verify our approach through simulation and hardware experiments. Finally, we extend our locomotion framework to deal with challenging tasks that comprise gap crossing, movement on …
Robert Bosch Centre for Cyber Physical Systems（罗伯特·博世网络物理系统中心）；Indian Institute of Science（印度科学学院）
In this paper, with a view toward fast deployment of locomotion gaits in low-cost hardware, we use a linear policy for realizing end-foot trajectories in the quadruped robot, Stoch $2$. In particular, the parameters of the end-foot trajectories are shaped via a linear feedback policy that takes the torso orientation and the terrain slope as inputs. The corresponding desired joint angles are obtained via an inverse kinematics solver and tracked via a PID control law. Augmented Random Search, a model-free and a gradient-free learning algorithm is used to train this linear policy. Simulation resu…
University of British Columbia（不列颠哥伦比亚大学）；NVIDIA（英伟达）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Model-free reinforcement learning (RL) for legged locomotion commonly relies on a physics simulator that can accurately predict the behaviors of every degree of freedom of the robot. In contrast, approximate reduced-order models are commonly used for many model predictive control strategies. In this work we abandon the conventional use of high-fidelity dynamics models in RL and we instead seek to understand what can be achieved when using RL with a much simpler centroidal model when applied to quadrupedal locomotion. We show that RL-based control of the accelerations of a centroidal model is s…
We present a legged motion planning approach for quadrupedal locomotion over challenging terrain. We decompose the problem into body action planning and footstep planning. We use a lattice representation together with a set of defined body movement primitives for computing a body action plan. The lattice representation allows us to plan versatile movements that ensure feasibility for every possible plan. To this end, we propose a set of rules that define the footstep search regions and footstep sequence given a body action. We use Anytime Repairing A* (ARA*) search that guarantees bounded subo…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；NVIDIA Research（英伟达研究院）；Princeton University（普林斯顿大学）；Purdue University（普渡大学）
This study introduces an analytically tractable and computationally efficient model of the legged robot dynamics associated with locomotion on a dynamic rigid surface (DRS), and develops a real-time motion planner based on the proposed model and its analytical solution. This study first theoretically extends the classical linear inverted pendulum (LIP) model from legged locomotion on a static surface to DRS locomotion, by relaxing the LIP's underlying assumption that the surface is static. The resulting model, which we call "DRS-LIP", is explicitly time-varying. After converting the DRS-LIP in…
Institute for Robotics and Intelligent Machines, Georgia Institute of Technology（佐治亚理工学院机器人与智能机器研究所）；MIT Biomimetic Robotics Lab（麻省理工学院仿生机器人实验室）；NAVER LABS（NAVER实验室）
In this letter, we present a versatile hierarchical offline planning algorithm, along with an online control pipeline for agile quadrupedal locomotion. Our offline planner alternates between optimizing centroidal dynamics for a reduced-order model and whole-body trajectory optimization, with the aim of achieving dynamics consensus. Our novel momentum-inertia-aware centroidal optimization, which uses an equimomental ellipsoid parameterization, is able to generate highly acrobatic motions via ``inertia shaping". Our whole-body optimization approach significantly improves upon the quality of stan…
Planning locomotion trajectories for legged microrobots is challenging because of their complex morphology, high frequency passive dynamics, and discontinuous contact interactions with their environment. Consequently, such research is often driven by time-consuming experimental methods. As an alternative, we present a framework for systematically modeling, planning, and controlling legged microrobots. We develop a three-dimensional dynamic model of a 1.5 gram quadrupedal microrobot with complexity (e.g., number of degrees of freedom) similar to larger-scale legged robots. We then adapt a recen…
Deep reinforcement learning (RL) uses model-free techniques to optimize task-specific control policies. Despite having emerged as a promising approach for complex problems, RL is still hard to use reliably for real-world applications. Apart from challenges such as precise reward function tuning, inaccurate sensing and actuation, and non-deterministic response, existing RL methods do not guarantee behavior within required safety constraints that are crucial for real robot scenarios. In this regard, we introduce guided constrained policy optimization (GCPO), an RL framework based upon our implem…
Virginia Tech（弗吉尼亚理工大学）；California Institute of Technology（加州理工学院）
This paper presents a layered control approach for real-time trajectory planning and control of robust cooperative locomotion by two holonomically constrained quadrupedal robots. A novel interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control architecture, two different model predictive control (MPC) algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The distributed MPC assumes two local quadra…
This paper aims to develop a hierarchical nonlinear control algorithm, based on model predictive control (MPC), quadratic programming (QP), and virtual constraints, to generate and stabilize locomotion patterns in a real-time manner for dynamical models of quadrupedal robots. The higher level of the proposed control scheme is developed based on an event-based MPC that computes the optimal center of mass (COM) trajectories for a reduced-order linear inverted pendulum (LIP) model subject to the feasibility of the net ground reaction force (GRF). The asymptotic stability of the desired target poi…
California Institute of Technology（加州理工学院）；ETH Zurich（苏黎世联邦理工学院）
Terrain-aware locomotion has become an emerging topic in legged robotics. However, it is hard to generate diverse, challenging, and realistic unstructured terrains in simulation, which limits the way researchers evaluate their locomotion policies. In this paper, we prototype the generation of a terrain dataset via terrain authoring and active learning, and the learned samplers can stably generate diverse high-quality terrains. We expect the generated dataset to make a terrain-robustness benchmark for legged locomotion. The dataset, the code implementation, and some policy evaluations are relea…
University of Edinburgh（爱丁堡大学）；University College London（伦敦大学学院）
This work developed a kernel-based residual learning framework for quadrupedal robotic locomotion. Initially, a kernel neural network is trained with data collected from an MPC controller. Alongside a frozen kernel network, a residual controller network is trained via reinforcement learning to acquire generalized locomotion skills and resilience against external perturbations. With this proposed framework, a robust quadrupedal locomotion controller is learned with high sample efficiency and controllability, providing omnidirectional locomotion at continuous velocities. Its versatility and robu…
Robotic Systems Lab, ETH Zurich（苏黎世联邦理工学院机器人系统实验室）；Robotics and Artificial Intelligence Lab, KAIST（韩国科学技术院机器人与人工智能实验室）；Intelligent Systems Lab, Intel（英特尔智能系统实验室）
Legged robots that can operate autonomously in remote and hazardous environments will greatly increase opportunities for exploration into under-explored areas. Exteroceptive perception is crucial for fast and energy-efficient locomotion: perceiving the terrain before making contact with it enables planning and adaptation of the gait ahead of time to maintain speed and stability. However, utilizing exteroceptive perception robustly for locomotion has remained a grand challenge in robotics. Snow, vegetation, and water visually appear as obstacles on which the robot cannot step~-- or are missing …
Robots operating in human environments need various skills, like slow and fast walking, turning, side-stepping, and many more. However, building robot controllers that can exhibit such a large range of behaviors is a challenging problem that requires tedious investigation for every task. We present a unified model-based control algorithm for imitating different animal gaits without expensive simulation training or real-world fine-tuning. Our method consists of stance and swing leg controllers using a centroidal dynamics model augmented with online adaptation techniques. We also develop a whole…
Whole-body Control (WBC) has emerged as an important framework in locomotion control for legged robots. However, most of WBC frameworks fail to generalize beyond rigid terrains. Legged locomotion over soft terrain is difficult due to the presence of unmodeled contact dynamics that WBCs do not account for. This introduces uncertainty in locomotion and affects the stability and performance of the system. In this paper, we propose a novel soft terrain adaptation algorithm called STANCE: Soft Terrain Adaptation and Compliance Estimation. STANCE consists of a WBC that exploits the knowledge of the …
Locomotion over soft terrain remains a challenging problem for legged robots. Most of the work done on state estimation for legged robots is designed for rigid contacts, and does not take into account the physical parameters of the terrain. That said, this letter answers the following questions: how and why does soft terrain affect state estimation for legged robots? To do so, we utilized a state estimator that fuses IMU measurements with leg odometry that is designed with rigid contact assumptions. We experimentally validated the state estimator with the HyQ robot trotting over both soft and …
Southern University of Science and Technology（南方科技大学）；University of Notre Dame（圣母大学）
This paper studies capturability and push recovery for quadrupedal locomotion. Despite the rich literature on capturability analysis and push recovery control for legged robots, existing tools are developed mainly for bipeds or humanoids. Distinct quadrupedal features such as point contacts and multiple swinging legs prevent direct application of these methods. To address this gap, we propose a switched systems model for quadruped dynamics, and instantiate the abstract viability concept for quadrupedal locomotion with a time-based gait. Capturability is characterized through a novel specificat…
Robotic Systems Lab, ETH Zürich（苏黎世联邦理工学院机器人系统实验室）
This paper addresses the problem of legged locomotion in non-flat terrain. As legged robots such as quadrupeds are to be deployed in terrains with geometries which are difficult to model and predict, the need arises to equip them with the capability to generalize well to unforeseen situations. In this work, we propose a novel technique for training neural-network policies for terrain-aware locomotion, which combines state-of-the-art methods for model-based motion planning and reinforcement learning. Our approach is centered on formulating Markov decision processes using the evaluation of dynam…
GenTe: Generative Real-world Terrains for General Legged Robot Locomotion Control
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）
Hierarchical Experience-informed Navigation for Multi-modal Quadrupedal Rebar Grid Traversal
Georgia Institute of Technology（佐治亚理工学院）；School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院机械工程学院）；SkyMul Inc（SkyMul公司）；School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电气与计算机工程学院）
Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）；University College London（伦敦大学学院）
This work developed a learning framework for perceptive legged locomotion that combines visual feedback, proprioceptive information, and active gait regulation of foot-ground contacts. The perception requires only one forward-facing camera to obtain the heightmap, and the active regulation of gait paces and traveling velocity are realized through our formulation of CPG-based high-level imitation of foot-ground contacts. Through this framework, an end-user has the ability to command task-level inputs to control different walking speeds and gait frequencies according to the traversal of differen…
Animals are capable of precise and agile locomotion using vision. Replicating this ability has been a long-standing goal in robotics. The traditional approach has been to decompose this problem into elevation mapping and foothold planning phases. The elevation mapping, however, is susceptible to failure and large noise artifacts, requires specialized hardware, and is biologically implausible. In this paper, we present the first end-to-end locomotion system capable of traversing stairs, curbs, stepping stones, and gaps. We show this result on a medium-sized quadruped robot using a single front-…
Load-bearing Assessment for Safe Locomotion of Quadruped Robots on Collapsing Terrain
Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia (IIT)（动态腿系统实验室，意大利技术研究院）；Department of Mechanical Engineering, São Carlos School of Engineering (EESC), University of São Paulo (USP)（机械工程系，圣卡洛斯工程学院（EESC），圣保罗大学）
