In this work, the Divergent Component of Motion (DCM) method is expanded to include angular coordinates for the first time. This work introduces the idea of spatial DCM, which adds an angular objective to the existing linear DCM theory. To incorporate the angular component into the framework, a discussion is provided on extending beyond the linear motion of the Linear Inverted Pendulum model (LIPM) towards the Single Rigid Body model (SRBM) for DCM. This work presents the angular DCM theory for a 1D rotation, simplifying the SRBM rotational dynamics to a flywheel to satisfy necessary linearity constraints. The 1D angular DCM is mathematically identical to the linear DCM and defined as an angle which is ahead of the current body rotation based on the angular velocity. This theory is combined into a 3D linear and 1D angular DCM framework, with discussion on the feasibility of simultaneously achieving both sets of objectives. A simulation in MATLAB and hardware results on the TORO humanoid are presented to validate the framework's performance.

For humans, fast, efficient walking over flat ground represents the vast majority of locomotion that an individual experiences on a daily basis, and for an effective, real-world humanoid robot the same will likely be the case. In this work, we propose a locomotion controller for efficient walking over near-flat ground using a relatively simple, model-based controller that utilizes a novel combination of several interesting design features including an ALIP-based step adjustment strategy, stance leg length control as an alternative to center of mass height control, and rolling contact for heel-to-toe motion of the stance foot. We then present the results of this controller on our robot Nadia, both in simulation and on hardware. These results include validation of this controller’s ability to perform fast, reliable forward walking at 0.75 m/s along with backwards walking, side-stepping, turning in place, and push recovery. We also present an efficiency comparison between the proposed control strategy and our baseline walking controller over three steady-state walking speeds. Lastly, we demonstrate some of the benefits of utilizing rolling contact in the stance foot, specifically the reduction of necessary positive and negative work throughout the stride.

Humanoid robots possess the ability to perform complex tasks in challenging environments. However, they require a model of the surroundings in a representation that is sufficient enough for downstream tasks such as footstep planning. The maps generated by existing mapping algorithms are either sparse, insufficient for footstep planning, memory intensive, or too slow for dynamic humanoid behaviors. In this work, we develop a mapping algorithm that combines planar region measurements along with kinematic-inertial state estimates to build a dense but efficient map of bounded planar surfaces. We present novel algorithms for plane feature matching, tracking and registration for mapping within a factor graph framework. The generated map is not only memory efficient, but also offers higher reliability and speed in bipedal footstep planning, than was possible earlier. The complete algorithm is also demonstrated using a full-scale humanoid robot, Nadia, walking over both flat ground and rough terrain utilizing the generated terrain map.

The ability to accomplish manipulation and locomotion tasks in the presence of significant time-varying external loads is a remarkable skill of humans that has yet to be replicated convincingly by humanoid robots. Such an ability will be a key requirement in the environments we envision deploying our robots: dull, dirty, and dangerous. External loads constitute a large model bias, which is typically unaccounted for. In this work, we enable our humanoid robot to engage in loco-manipulation tasks in the presence of significant model bias due to external loads. We propose an online estimation and control framework involving the combination of a physically consistent extended Kalman filter for inertial parameter estimation coupled to a whole-body controller. We showcase our results both in simulation and in hardware, where weights are mounted on Nadia’s wrist links as a proxy for engaging in tasks where large external loads are applied to the robot.

Complex multibody legged robots can have complex rotational control challenges. In this paper, we propose a concise way to understand and formulate a whole-body orientation that (i) depends on system configuration only and not a history of motion, (ii) can be representative of the orientation of the entire system while not being attached to any specific link, and (iii) has a rate of change that approximates total system angular momentum. We relate this orientation coordinate to past work, and discuss and demonstrate, including on hardware, several different uses for it.

Manual materials handling occupations often involve repetitive lifting, lowering, and carrying motions, which can lead to muscular fatigue and/or injury. The risk increases when loads must be worn on the body for the entirety of a job shift. Exoskeletons have been developed to assist these types of motions, but require the user to bear the weight of a load through their body. Load carriage exoskeletons have been developed to offload worn mass from the user to the ground through the device structure, but they have had limited success and have not been well studied in manual materials handling tasks. In this paper, we introduce a hip-knee-ankle exoskeleton and two control methods: virtual model control and gravity compensation. We compared the ability of each controller to reduce lower-limb muscle activity during squatting. Because the virtual model controller is tailored to squatting, we hypothesized that it would outperform gravity compensation. Both controllers were able to reduce the activity of major lower-limb muscle groups during squatting when compared to squatting with the exoskeleton turned off. Contrary to our original hypothesis, the gravity compensation controller generally outperformed the virtual model controller, which may have been caused by the gravity compensation controller having more consistent knee torque application and the virtual model controller requiring better per-user tuning and familiarization. These results indicate the efficacy of both controllers in reducing injury risk in the lower limbs during squatting.

For achieving significant levels of autonomy, legged robot behaviors require perceptual awareness of both the terrain for traversal, as well as structures and objects in their surroundings for planning, obstacle avoidance, and high-level decision making. In this work, we present a perception engine for legged robots that extracts the necessary information for developing semantic, contextual, and metric awareness of their surroundings. Our custom sensor configuration consists of (1) an active depth sensor, (2) two monocular cameras looking sideways, (3) a passive stereo sensor observing the terrain, (4) a forward facing active depth camera, and (5) a rotating 3D LIDAR with a large vertical field-of-view (FOV). The mutual overlap in the sensors' FOVs allows us to redundantly detect and track objects of both dynamic and static types. We fuse class masks generated by a semantic segmentation model with LIDAR and depth data to accurately identify and track individual instances of dynamically moving objects. In parallel, active depth and passive stereo streams of the terrain are also fused to map the terrain using the on-board GPU. We evaluate the engine using two different humanoid behaviors, (1) look-and-step and (2) track-and-follow, on the Boston Dynamics Atlas.

Obtaining highly dynamic motions in robots is a difficult task. In recent years, sophistication in mechanical design, improved algorithms, and high computational power allows new robots to perform natural gaits and dynamic motions such as backflips. Offline optimization is often necessary to obtain good performance in those difficult motions. However, when an athlete does a backflip, he will adapt “online” to any change, and that is shown in the robustness of the movements. One of the biggest challenges in robotics is to perform those movements using online optimization with the dynamics of the robot. Here, we present an approach to deal with complicated tasks using online optimization. We obtain 90° rotational jumps and jumps over sloped terrain in the Mini-Cheetah hardware, and online-optimized backflips, sideflips, and frontflips in a real-time physical simulator with full-body dynamics.

Legged robots require fast and accurate representation of their surrounding terrain to achieve behaviors such as running, push recovery, continuous walking, backflips, while also utilizing on-board computational resources efficiently. The desired tasks can be achieved efficiently by representing the environment using planar regions. However, existing methods for planar region extraction are either too slow or require significant compute time on the Central Processing Unit (CPU). In this work we exploit key properties of depth images and Graphical Processing Unit (GPU) to estimate planar regions around the robot at very high frame rates of 150-200 Hz. The proposed algorithm uses a set of fully customizable and interchangeable set of kernel layers on the GPU to process the depth map in parallel and generate a locally connected graph structure, which is later separated into planar components using a basic depth-first search. We test the proposed algorithm on the Atlas robot while performing different walking behaviors on oriented cinder blocks, as well as in simulation with simulated sensor and robot. The algorithm is open-sourced for research on legged robots and other fields.

Awareness of the environment is essential for mobile robots. Perception for legged robots requires high levels of reliability and accuracy in order to walk stably in the types of complex, cluttered environments we are interested in. In this paper, we present a usable environmental perception algorithm designed to detect steppable areas and obstacles for the autonomous generation of desired footholds for legged robots. To produce an efficient representation of the environment, the proposed perception algorithm is desired to cluster point cloud data to planar regions composed of convex polygons. We describe in this paper the end-to-end pipeline from data collection to generation of the regions, where we first compose an octree in order to create a more efficient data representation. We then group the leaves in the tree using a nearest neighbor search into a planar region, which is composed of the concave hull of points that is decomposed into convex polygons. We present a variety of environments, and illustrate the usability of this approach by the Atlas humanoid robots walking over rough terrain. We also discuss various challenges we faced and insights we gained in the development of this approach.

Performing large step-ups is a challenging task for a humanoid robot. It requires the robot to perform motions at the limit of its reachable workspace while straining to move its body upon the obstacle. This paper presents a non-linear trajectory optimization method for generating step-up motions. We adopt a simplified model of the centroidal dynamics to generate feasible Center of Mass trajectories aimed at reducing the torques required for the step-up motion. The activation and deactivation of contacts at both feet are considered explicitly. The output of the planner is a Center of Mass trajectory plus an optimal duration for each walking phase. These desired values are stabilized by a whole-body controller that determines a set of desired joint torques. We experimentally demonstrate that by using trajectory optimization techniques, the maximum torque required to the full-size humanoid robot Atlas can be reduced up to 20% when performing a step-up motion.

We present an approach for achieving a natural, efficient gait on bipedal robots using straightened legs and toe-off. Our algorithm avoids complex height planning by allowing a whole-body controller to determine the straightest possible leg configuration at run-time. The controller solutions are biased towards a straight leg configuration by projecting leg joint angle objectives into the null-space of the other quadratic program motion objectives. To allow the legs to remain straight throughout the gait, toe-off was utilized to increase the kinematic reachability of the legs. The toe-off motion is achieved through underconstraining the foot position, allowing it to emerge naturally. We applied this approach of under-specifying the motion objectives to the Atlas humanoid, allowing it to walk over a variety of terrain. We present both experimental and simulation results and discuss performance limitations and potential improvements.

When walking at high speeds, the swing legs of robots produce a non-negligible angular momentum rate. To accommodate this, we provide a reference trajectory generator for bipedal walking that incorporates predicted centroidal angular momentum at the planning stage. This can be done efficiently as the Centroidal Moment Pivot (CMP), Instantaneous Capture Point (ICP) and the center of mass (CoM) all have closed-form trajectory solutions due to their linear dynamics. This is then used to produce smooth, continuous trajectories. We furthermore provide a lightweight model to estimate angular momentum as induced during leg swing of the gait cycle. Our proposed trajectory generator is tested thoroughly in simulation and has been shown to successfully operate on the real hardware.

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional “ankle strategy” balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements.

This paper presents an extension of previous model predictive control (MPC) schemes to the stabilization of the time-varying divergent component of motion (DCM). To address the control authority limitations caused by fixed footholds, the step positions and rotations are treated as control inputs, allowing the generation and execution of stable walking motions, both at high speeds and in the face of disturbances. Rotation approximations are handled by applying a mixed-integer program, which, when combined with the use of the time-varying DCM to account for the effects of height changes, improve the versatility of MPC. Simulation results of fast walking and step recovery with the ESCHER humanoid demonstrate the effectiveness of this approach.

To operate in human environments, robots must be able to withstand external disturbances. Small disturbances can be stabilized through momentum regulation, but larger ones require steps to prevent falling. This work presents two new techniques for disturbance rejection. The first is an extension of divergent component of motion (DCM) and capture point tracking controllers that augments a PI feedback control law with a disturbance observer. This is used to estimate transient disturbances through momentum-rate-of-change error. For larger disturbances, we present a novel optimization-based framework based on the DCM dynamics that uses a quadratic program to compute the desired ground reaction forces and recovery step location. Using optimization gives a flexibility that enables planning angular-momentum-rate-of-change trajectories to help reduce recovery step length. We then illustrate the effectiveness of these methods with hardware and simulation experiments of the THOR humanoid.