The enhanced mobility brought by legged locomotion empowers quadrupedal robots to navigate through complex and unstructured environments. However, optimizing agile locomotion while accounting for the varying energy costs of traversing different terrains remains an open challenge. Most previous work focuses on planning trajectories with traversability cost estimation based on human-labeled environmental features. This human-centric approach is insufficient because it does not account for the varying capabilities of the robot locomotion controllers over challenging terrains. To address this, we introduce a novel real-world learning pipeline that unifies offline demonstrations, online reinforcement learning, and multi-modal perception to achieve robust legged navigation. The framework employs multiple training stages to develop a planner that guides the robot in avoiding obstacles and hardto- traverse terrains while reaching its goals. We first develop a novel traversability estimator in a robot-centric manner. The training of the navigation planner is directly performed in the real world using a sample efficient reinforcement learning method. With the proposed method, a quadrupedal robot learns to perform traversability-aware navigation through realworld interactions in diverse offroad and unstructured environments. Moreover, the robot demonstrates the ability to generalize the learned navigation skills to unseen scenarios.

Model Predictive Control (MPC) relies heavily on the robot model for its control law. However, a gap always exists between the reduced-order control model with uncertainties and the real robot, which degrades its performance. To address this issue, we propose the controller of integrating a data-driven error model into traditional MPC for quadruped robots. Our approach leverages real-world data from sensors to compensate for defects in the control model. Specifically, we employ the Autoregressive Moving Average Vector (ARMAV) model to construct the state error model of the quadruped robot using data. The predicted state errors are then used to adjust the predicted future robot states generated by MPC. By such an approach, our proposed controller can provide more accurate inputs to the system, enabling it to achieve desired states even in the presence of model parameter inaccuracies or disturbances. The proposed controller exhibits the capability to partially eliminate the disparity between the model and the real-world robot, thereby enhancing the locomotion performance of quadruped robots. We validate our proposed method through simulations and real-world experimental trials on a large-size quadruped robot that involves carrying a 20 kg un-modeled payload (84% of body weight).

Exploring the limits of quadruped robot agility, particularly in the context of rapid and real-time planning and execution of omnidirectional jump trajectories, presents significant challenges due to the complex dynamics involved, especially when considering significant impulse contacts. This paper introduces a new framework to enable fast, omnidirectional jumping capabilities for quadruped robots. Utilizing minimum jerk technology, the proposed framework efficiently generates jump trajectories that exploit its analytical solutions, ensuring numerical stability and dynamic compatibility with minimal computational resources. The virtual model control is employed to formulate a Quadratic Programming (QP) optimization problem to accurately track the Center of Mass (CoM) trajectories during the jump phase. The whole-body control strategies facilitate precise and compliant landing motion. Moreover, the different jumping phase is triggered by time-schedule. The framework’s efficacy is demonstrated through its implementation on an enhanced version of the open-source Mini Cheetah robot. Omnidirectional jumps-including forward, backward, and other directional-were successfully executed, showcasing the robot’s capability to perform rapid and consecutive jumps with an average trajectory generation and tracking solution time of merely 50 microseconds.

Offline evolutionary-based methodologies have supplied a successful motion planning framework for the quadrupedal jump. However, the time-consuming computation caused by massive population evolution in offline evolutionary-based jumping framework significantly limits the popularity in the quadrupedal field. This paper presents a time-friendly online motion planning framework based on meta-heuristic Differential evolution (DE), Latin hypercube sampling, and Configuration space (DLC). The DLC framework establishes a multidimensional optimization problem leveraging centroidal dynamics to determine the ideal trajectory of the center of mass (CoM) and ground reaction forces (GRFs). The configuration space is introduced to the evolutionary optimization in order to condense the searching region. Latin hypercube sampling offers more uniform initial populations of DE under limited sampling points, accelerating away from a local minimum. This research also constructs a collection of pre-motion trajectories as a warm start when the objective state is in the neighborhood of the pre-motion state to drastically reduce the solving time. The proposed methodology is successfully validated via real robot experiments for online jumping trajectory optimization with different jumping motions (e.g., ordinary jumping, flipping, and spinning).

This paper presents an optimal motion planning framework to generate versatile energy-optimal quadrupedal jumping motions automatically (e.g., flips, spin). The jumping motions via the centroidal dynamics are formulated as a 12-dimensional black-box optimization problem subject to the robot kino-dynamic constraints. Gradient-based approaches offer great success in addressing trajectory optimization (TO), yet, prior knowledge (e.g., reference motion, contact schedule) is required and results in sub-optimal solutions. The new proposed framework first employed a heuristics-based optimization method to avoid these problems. Moreover, a prioritization fitness function is created for heuristics-based algorithms in robot ground reaction force (GRF) planning, enhancing convergence and searching performance considerably. Since heuristics-based algorithms often require significant time, motions are planned offline and stored as a pre-motion library. A selector is designed to automatically choose motions with user-specified or perception information as input. The proposed framework has been successfully validated only with a simple continuously tracking PD controller in an open-source Mini-Cheetah by several challenging jumping motions, including jumping over a window-shaped obstacle with 30 cm height and left-flipping over a rectangle obstacle with 27 cm height. (Video*)