We propose an online motion planner for legged robot locomotion with the primary objective of achieving energy efficiency. The conceptual idea is to leverage a placement set of footstep positions based on the robot's body position to determine when and how to execute steps. In particular, the proposed planner uses virtual placement sets beneath the hip joints of the legs and executes a step when the foot is outside of such placement set. Furthermore, we propose a parameter design framework that considers both energy-efficiency and robustness measures to optimize the gait by changing the shape of the placement set along with other parameters, such as step height and swing time, as a function of walking speed. We show that the planner produces trajectories that have a low Cost of Transport (CoT) and high robustness measure, and evaluate our approach against model-free Reinforcement Learning (RL) and motion imitation using biological dog motion priors as the reference. Overall, within low to medium velocity range, we show a 50.4% improvement in CoT and improved robustness over model-free RL, our best performing baseline. Finally, we show ability to handle slippery surfaces, gait transitions, and disturbances in simulation and hardware with the Unitree A1 robot.

State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: https://github.com/AlexS28/OptiState

This paper presents SCALER, a versatile free-climbing multi-limbed robot that is designed to achieve tightly coupled simultaneous locomotion and dexterous grasping. Although existing quadruped-limbed robots have shown impressive dexterous skills such as object manipulation, it is essential to balance power-intensive locomotion and dexterous grasping capabilities. We design a torso linkage and a parallel-serial limb to meet such conflicting skills that pose unique challenges in the hardware designs. SCALER employs underactuated two-fingered GOAT grippers that can mechanically adapt and offer 7 modes of grasping, enabling SCALER to traverse extreme terrains with multi-modal grasping strategies. We study the whole-body approach, where SCALER uses its body and limbs to generate additional forces for stable grasping with environments, further enhancing versatility. Furthermore, we improve the GOAT gripper actuation speed to realize more dynamic climbing in a closed-loop control fashion. With these proposed technologies, SCALER can traverse vertical, overhang, upside-down, slippery terrains, and bouldering walls with non-convex-shaped climbing holds under the Earth's gravity.

In multi-point contact systems, precise force control is crucial for achieving stable and safe interactions between robots and their environment. Thus, we demonstrate an admittance controller with auto-tuning that can be applied for these systems. The controller's objective is to track the target wrench profiles of each contact point while considering the additional torque due to rotational friction. Our admittance controller is adaptive during online operation by using an auto-tuning method that tunes the gains of the controller while following user-specified training objectives. These objectives include facilitating controller stability, such as tracking the wrench profiles as closely as possible, ensuring control outputs are within force limits that minimize slippage, and avoiding configurations that induce kinematic singularity. We demonstrate the robustness of our controller on hardware for both manipulation and locomotion tasks using a multi-limbed climbing robot.

Achieving highly accurate dynamic or simulator models that are close to the real robot can facilitate model-based controls (e.g., model predictive control or linear-quadradic regulators), model-based trajectory planning (e.g., trajectory optimization), and decrease the amount of learning time necessary for reinforcement learning methods. Thus, the objective of this work is to learn the residual errors between a dynamic and/or simulator model and the real robot. This is achieved using a neural network, where the parameters of a neural network are updated through an Unscented Kalman Filter (UKF) formulation. Using this method, we model these residual errors with only small amounts of data -- a necessity as we improve the simulator/dynamic model by learning directly from real-world operation. We demonstrate our method on robotic hardware (e.g., manipulator arm, and a wheeled robot), and show that with the learned residual errors, we can further close the reality gap between dynamic models, simulations, and actual hardware.

This paper introduces SCALER, a quadrupedal robot that demonstrates climbing on bouldering walls, overhangs, ceilings and trotting on the ground. SCALER is one of the first high-degrees of freedom four-limbed robots that can free-climb under the Earth's gravity and one of the most mechanically efficient quadrupeds on the ground. Where other state-of-the-art climbers specialize in climbing, SCALER promises practical free-climbing with payload \textit{and} ground locomotion, which realizes true versatile mobility. A new climbing gait, SKATE gait, increases the payload by utilizing the SCALER body linkage mechanism. SCALER achieves a maximum normalized locomotion speed of $1.87$ /s, or $0.56$ m/s on the ground and $1.0$ /min, or $0.35$ m/min in bouldering wall climbing. Payload capacity reaches $233$ % of the SCALER weight on the ground and $35$ % on the vertical wall. Our GOAT gripper, a mechanically adaptable underactuated two-finger gripper, successfully grasps convex and non-convex objects and supports SCALER.

While motion planning of locomotion for legged robots has shown great success, motion planning for legged robots with dexterous multi-finger grasping is not mature yet. We present an efficient motion planning framework for simultaneously solving locomotion (e.g., centroidal dynamics), grasping (e.g., patch contact), and contact (e.g., gait) problems. To accelerate the planning process, we propose distributed optimization frameworks based on Alternating Direction Methods of Multipliers (ADMM) to solve the original large-scale Mixed-Integer NonLinear Programming (MINLP). The resulting frameworks use Mixed-Integer Quadratic Programming (MIQP) to solve contact and NonLinear Programming (NLP) to solve nonlinear dynamics, which are more computationally tractable and less sensitive to parameters. Also, we explicitly enforce patch contact constraints from limit surfaces with micro-spine grippers. We demonstrate our proposed framework in the hardware experiments, showing that the multi-limbed robot is able to realize various motions including free-climbing at a slope angle 45{\deg} with a much shorter planning time.