This paper proposes a kinodynamic motion planning framework for multi-legged robot jumping based on the mixed-integer convex program (MICP), which simultaneously reasons about centroidal motion, contact points, wrench, and gait sequences. This method uniquely combines configuration space discretization and the construction of feasible wrench polytope (FWP) to encode kinematic constraints, actuator limit, friction cone constraint, and gait sequencing into a single MICP. The MICP could be efficiently solved to the global optimum by off-the-shelf numerical solvers and provide highly dynamic jumping motions without requiring initial guesses. Simulation and experimental results demonstrate that the proposed method could find novel and dexterous maneuvers that are directly deployable on the two-legged robot platform to traverse through challenging terrains.
Performing highly agile dynamic motions, such as jumping or running on uneven stepping stones has remained a challenging problem in legged robot locomotion. This paper presents a framework that combines trajectory optimization and model predictive control to perform robust and consecutive jumping on stepping stones. In our approach, we first utilize trajectory optimization based on full-nonlinear dynamics of the robot to generate periodic jumping trajectories for various jumping distances. A jumping controller based on a model predictive control is then designed for realizing smooth jumping tr…
Dynamic jumping with legged robots poses a challenging problem in planning and control. Formulating the jump optimization to allow fast online execution is difficult; efficiently using this capability to generate long-horizon motion plans further complicates the problem. In this work, we present a hierarchical planning framework to address this problem. We first formulate a real-time tractable trajectory optimization for performing omnidirectional jumping. We then embed the results of this optimization into a low dimensional jump feasibility classifier. This classifier is leveraged to produce …
This paper reports on developing an integrated framework for safety-aware informative motion planning suitable for legged robots. The information-gathering planner takes a dense stochastic map of the environment into account, while safety constraints are enforced via Control Barrier Functions (CBFs). The planner is based on the Incrementally-exploring Information Gathering (IIG) algorithm and allows closed-loop kinodynamic node expansion using a Model Predictive Control (MPC) formalism. Robotic exploration and information gathering problems are inherently path-dependent problems. That is, the …
Southern University of Science and Technology（南方科技大学）；National University of Singapore（新加坡国立大学）；University of Notre Dame（圣母大学）
This paper studies jumping for wheeled-bipedal robots, a motion that takes full advantage of the benefits from the hybrid wheeled and legged design features. A comprehensive hierarchical scheme for motion planning and control of jumping with wheeled-bipedal robots is developed. Underactuation of the wheeled-bipedal dynamics is the main difficulty to be addressed, especially in the planning problem. To tackle this issue, a novel wheeled-spring-loaded inverted pendulum (W-SLIP) model is proposed to characterize the essential dynamics of wheeled-bipedal robots during jumping. Relying on a differe…
Tandon School of Engineering, New York University（纽约大学坦登工程学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Whole-body optimizers have been successful at automatically computing complex dynamic locomotion behaviors. However they are often limited to offline planning as they are computationally too expensive to replan with a high frequency. Simpler models are then typically used for online replanning. In this paper we present a method to generate whole body movements in real-time for locomotion tasks. Our approach consists in learning a centroidal neural network that predicts the desired centroidal motion given the current state of the robot and a desired contact plan. The network is trained using an…
University of Notre Dame（圣母大学）；Robotics at Google（谷歌机器人部门）
Specialized motions such as jumping are often achieved on quadruped robots by solving a trajectory optimization problem once and executing the trajectory using a tracking controller. This approach is in parallel with Model Predictive Control (MPC) strategies that commonly control regular gaits via online re-planning. In this work, we present a nonlinear MPC (NMPC) technique that unlocks on-the-fly re-planning of specialized motion skills and regular locomotion within a unified framework. The NMPC reasons about a hybrid kinodynamic model, and is solved using a variant of a constrained Different…
School of Informatics, The University of Edinburgh（爱丁堡大学信息学院）；Shenzhen Institute for Artificial Intelligence and Robotics for Society (AIRS)（深圳市人工智能与机器人研究院）；Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
In this paper, we study a wheeled robot with a prismatic extension joint. This allows the robot to build up momentum to perform jumps over obstacles and to swing up to the upright position after the loss of balance. We propose a template model for the class of such two-wheeled jumping robots. This model can be considered as the simplest wheeled-legged system. We provide an analytical derivation of the system dynamics which we use inside a model predictive controller (MPC). We study the behavior of the model and demonstrate highly dynamic motions such as swing-up and jumping. Furthermore, these…
Performing highly agile acrobatic motions with a long flight phase requires perfect timing, high accuracy, and coordination of the full-body motion. To address these challenges, we present a novel approach on timings and trajectory optimization framework for legged robots performing aggressive 3D jumping. In our method, we firstly utilize an effective optimization framework using simplified rigid body dynamics to solve for contact timings and a reference trajectory of the robot body. The solution of this module is then used to formulate a full-body trajectory optimization based on the full non…
In this article, we show that learned policies can be applied to solve legged locomotion control tasks with extensive flight phases, such as those encountered in space exploration. Using an off-the-shelf deep reinforcement learning algorithm, we trained a neural network to control a jumping quadruped robot while solely using its limbs for attitude control. We present tasks of increasing complexity leading to a combination of three-dimensional (re-)orientation and landing locomotion behaviors of a quadruped robot traversing simulated low-gravity celestial bodies. We show that our approach easil…
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）
Versatile, Robust, and Explosive Locomotion with Rigid and Articulated Compliant Quadrupeds
Cognitive Robotics, Delft University of Technology（代尔夫特理工大学认知机器人学系）；University of Trento（特伦托大学）；University of Manchester（曼彻斯特大学）；Institute of Robotics and Mechatronics, German Aerospace Center (DLR)（德国航空航天中心机器人与机电一体化研究所）
Princeton University（普林斯顿大学）；Google Research（谷歌研究院）；Georgia Institute of Technology（佐治亚理工学院）
Designing control policies for legged locomotion is complex due to the under-actuated and non-continuous robot dynamics. Model-free reinforcement learning provides promising tools to tackle this challenge. However, a major bottleneck of applying model-free reinforcement learning in real world is safety. In this paper, we propose a safe reinforcement learning framework that switches between a safe recovery policy that prevents the robot from entering unsafe states, and a learner policy that is optimized to complete the task. The safe recovery policy takes over the control when the learner polic…
Locomotion for legged robots poses considerable challenges when confronted by obstacles and adverse environments. Footstep planners are typically only designed for one mode of locomotion, but traversing unfavorable environments may require several forms of locomotion to be sequenced together, such as walking, crawling, and jumping. Multi-modal motion planners can be used to address some of these problems, but existing implementations tend to be time-consuming and are limited to quasi-static actions. This paper presents a motion planning method to traverse complex environments using multiple ca…
University of Louisiana at Lafayette（路易斯安那大学拉斐特分校）
Legged systems have many advantages when compared to their wheeled counterparts. For example, they can more easily navigate extreme, uneven terrain. However, there are disadvantages as well, particularly the difficulty seen in modeling the nonlinearities of the system. Research has shown that using flexible components within legged locomotive systems improves performance measures such as efficiency and running velocity. Because of the difficulties encountered in modeling flexible systems, control methods such as reinforcement learning can be used to define control strategies. Furthermore, rein…
Quadrupeds for Planetary Exploration: Field Testing Control Algorithms on an Active Volcano
Robotics Innovation Center, DFKI GmbH（机器人创新中心，DFKI GmbH）；German Aerospace Center, Institute of Space Systems（德国航空航天中心，空间系统研究所）；University of Bremen（不莱梅大学）
Saratoga High School（萨拉托加高中）；University of Michigan（密歇根大学）
We propose a mechanically simple and cheap design for a series elastic actuator with controllable stiffness. Such characteristics are necessary for animals for running, jumping, throwing, and manipulation, yet in robots, variable stiffness actuators are either complicated or mimicked at low bandwidth through feedback controllers. A robust and simple design is needed to build reliable and cheap robots with animal capabilities. The key insight of our design is attaching torsional springs to timing belts to create a variable stiffness linear spring. In an antagonistic pair, varying the distance b…
Locomotion for legged robots poses considerable challenges when confronted by obstacles and adverse environments. Footstep planners are typically only designed for one mode of locomotion, but traversing unfavorable environments may require several forms of locomotion to be sequenced together, such as walking, crawling, and jumping. Multi-modal motion planners can be used to address some of these problems, but existing implementations tend to be time-consuming and are limited to quasi-static actions. This paper presents a motion planning method to traverse complex environments using multiple ca…
University of Tokyo（东京大学）；California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）
Although ground robotic autonomy has gained widespread usage in structured and controlled environments, autonomy in unknown and off-road terrain remains a difficult problem. Extreme, off-road, and unstructured environments such as undeveloped wilderness, caves, and rubble pose unique and challenging problems for autonomous navigation. To tackle these problems we propose an approach for assessing traversability and planning a safe, feasible, and fast trajectory in real-time. Our approach, which we name STEP (Stochastic Traversability Evaluation and Planning), relies on: 1) rapid uncertainty-awa…
SF-TIM: A Simple Framework for Enhancing Quadrupedal Robot Jumping Agility by Combining Terrain Imagination and Measurement
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, China（浙江大学现代光学仪器国家重点实验室）；School of Artificial Intelligence and Robotics and National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University, China（湖南大学人工智能与机器人学院和机器人视觉感知与控制技术国家工程研究中心）；State Key Laboratory of Industrial Control Technology, Zhejiang University, China（浙江大学工业控制技术国家重点实验室）；DeepRobotics Co. Ltd., China（深睿科技有限公司）
Despite many accomplishments by legged robot designers, state-of-the-art bipedal robots are prone to falling over, cannot negotiate extremely rough terrains and cannot directly regulate unilateral contact forces. Our objective is to integrate merits of legged and aerial robots in a single platform. We will show that the thrusters in a bipedal legged robot called Harpy can be leveraged to stabilize the robot's frontal dynamics and permit jumping over large obstacles which is an unusual capability not reported before. In addition, we will capitalize on the thrusters action in Harpy and will show…
Our paper proposes a model predictive controller as a single-task formulation that simultaneously optimizes wheel and torso motions. This online joint velocity and ground reaction force optimization integrates a kinodynamic model of a wheeled quadrupedal robot. It defines the single rigid body dynamics along with the robot's kinematics while treating the wheels as moving ground contacts. With this approach, we can accurately capture the robot's rolling constraint and dynamics, enabling automatic discovery of hybrid maneuvers without needless motion heuristics. The formulation's generality thro…
Imperial College London（伦敦帝国理工学院）；University of Edinburgh（爱丁堡大学）
To achieve highly dynamic jumps of legged robots, it is essential to control the rotational dynamics of the robot. In this paper, we aim to improve the jumping performance by proposing a unified model for planning highly dynamic jumps that can approximately model the centroidal inertia. This model abstracts the robot as a single rigid body for the base and point masses for the legs. The model is called the Lump Leg Single Rigid Body Model (LL-SRBM) and can be used to plan motions for both bipedal and quadrupedal robots. By taking the effects of leg dynamics into account, LL-SRBM provides a com…
