Running and jumping are locomotion modes that allow legged robots to rapidly traverse great distances and overcome difficult terrain. In this article, we show that the 3-D divergent component of motion (3D-DCM) framework, which was successfully used for generating walking trajectories in previous works, retains its validity and coherence during flight phases, and, therefore, can be used for planning running and jumping motions. We propose a highly efficient motion planner that generates stable center-of-mass (CoM) trajectories for running and jumping with arbitrary contact sequences and time parametrizations. The proposed planner constructs the complete motion plan as a sequence of motion phases that can be of different types: stance, flight, transition phases, etc. We introduce a unified formulation of the CoM and DCM waypoints at the start and end of each motion phase, which makes the framework extensible and enables the efficient waypoint computation in matrix and algorithmic form. The feasibility of the generated reference trajectories is demonstrated by extensive whole-body simulations with the humanoid robot TORO.

Embedding elastic elements into legged robots through mechanical design enables highly efficient oscillating patterns that resemble natural gaits. However, current trajectory planning techniques miss the opportunity of taking advantage of these natural motions. This work proposes a locomotion planning method that aims to unify traditional trajectory generation with modal oscillations. Our method utilizes task-space linearized modes for generating center of mass trajectories on the sagittal plane. We then use nonlinear optimization to find the gait timings that match these trajectories within the Divergent Component of Motion planning framework. This way, we can robustly translate the modes-aware centroidal motions into joint coordinates. We validate our approach with promising results and insights through experiments on a compliant quadrupedal robot.

Gait generation frameworks for humanoid robots typically assume a constant centroidal angular momentum (CAM) throughout the walking cycle, which induces undesirable contact torques in the feet and results in performance degradation. In this work, we present a novel algorithm to learn the CAM online and include the obtained knowledge within the closed-form solutions of the Divergent Component of Motion (DCM) locomotion framework. To ensure a reduction of the contact torques at the desired center of pressure position, a CAM trajectory is generated and explicitly tracked by a whole-body controller. Experiments with the humanoid robot TORO demonstrate that the proposed method significantly increases the maximum step length and walking speed during locomotion.

In this paper, we present a highly efficient Divergent Component of Motion (DCM) reference trajectory generator capable of adapting online to large perturbations acting on the center-of-mass (push recovery) and on the swing foot (stumble recovery). For push recovery, we propose an analytic solution for a footstep adjustment strategy based on the DCM dynamics. The proposed algorithm considers double support phases explicitly and is active throughout the motion, i.e., during both single and double support phases. For stumble recovery, we introduce a continuous DCM trajectory adaptation based on the instantaneous tracking error of the swing foot. Our method is highly efficient, computing a push recovery solution within 10 microseconds on the robot hardware. Furthermore, it achieves robust locomotion for large external perturbations, which we demonstrate in simulations and experiments with the humanoid robot TORO.

This paper presents methods that facilitate the implementation of dynamic walking on torque-controlled robots in real world experiments. The work uses the Divergent Component of Motion (DCM) for walking trajectory generation and control. The DCM controller is embedded into a whole-body controller (WBC) that produces a full-body walking behavior. While in simulation the combination of DCM and WBC is sufficient for achieving sophisticated walking gaits, during our initial experiments several real-world issues, detailed in this paper, prevented the original control framework from functioning. This work presents the improvements to the original control framework that enabled a breakthrough on the way to achieving torque-based dynamic walking on a real robot.

This paper presents a hierarchical path planner consisting of two stages: a global planner that uses workspace information to create collision-free paths for the robot end-effector to follow, and multiple local planners running in parallel that verify the paths in the configuration space by expanding a task-space rapidly-exploring random tree (RRT). We demonstrate the practicality of our approach by comparing it with state-of-the-art planners in several challenging path planning problems. While using a single tree, our planner outperforms other single tree approaches in task-space or configuration space (C-space), while its performance and robustness are comparable to or better than that of parallelized bidirectional C-space planners.

This paper presents a new method for planning and controlling dynamic multi-contact motions for humanoid robots. Our motion planner takes a sequence of multi-contact stances and generates closed-form reference trajectories for the robot center of mass (CoM) position, velocity, and acceleration, based on the concept of Divergent Component of Motion (DCM). The timing of the contact transitions and the end-effector trajectories are automatically computed such that the motion is feasible with respect to kinematic and dynamic constraints. We verify the constraints using a simplified model of the robot to achieve a very fast planner that finds a feasible solution within a few seconds. The reference trajectories serve as inputs to a passivity-based whole-body controller which includes a DCM controller for tracking the CoM trajectory. We demonstrate the robustness of our approach in simulation and experiments with the humanoid robot TORO.

This paper presents a novel multi-step closed-form walking trajectory generator based on the concept of Divergent Component of Motion (DCM) that guarantees smoothness of all resulting reference trajectories. Further, we introduce an analytical method for footstep adjustment to recover from strong disturbances. The DCM trajectory is adjusted to guarantee smoothness of control outputs. Additionally, we present a momentum-based disturbance observer that improves robustness w.r.t. strong continuous perturbations. The proposed methods are verified in simulations.