As legged robots continue to evolve, new control methods are being developed to provide fast, robust, accurate and computationally efficient algorithms for traversing challenging environments. This paper presents a realtime adaptive locomotion controller for quadrupeds, designed to maintain stability and controllability on various surfaces, including highly slippery terrains. The proposed approach optimizes control effort distribution based on the probability of slippage by utilizing a surface-independent adaptation layer. By balancing the robot's redundant kinematic system through rank relaxation-similar to loosening constraints in optimization problems-this method demonstrates significant performance improvements. Unlike Reinforcement Learning (RL) approaches, which depend on pre-trained policies and may struggle to adapt velocity tracking control across different terrains, our method rapidly adjusts to changing conditions, as validated by extensive simulation experiments.

Legged robot navigation in unstructured and slippery terrains depends heavily on the ability to accurately identify the quality of contact between the robot's feet and the ground. Contact state estimation is regarded as a challenging problem and is typically addressed by exploiting force measurements, joint encoders and/or robot kinematics and dynamics. In contrast to most state of the art approaches, the current work introduces a novel probabilistic method for estimating the contact state based solely on proprioceptive sensing, as it is readily available by Inertial Measurement Units (IMUs) mounted on the robot's end effectors. Capitalizing on the uncertainty of IMU measurements, our method estimates the probability of stable contact. This is accomplished by approximating the multimodal probability density function over a batch of data points for each axis of the IMU with Kernel Density Estimation. The proposed method has been extensively assessed against both real and simulated scenarios on bipedal and quadrupedal robotic platforms such as ATLAS, TALOS and Unitree's GO1.

In this work, the utilization of Dirichlet (periodic sinc) base functions in DMPs for encoding periodic motions is proposed. By utilizing such kernels, we are able to analytically compute the minimum required number of kernels based only on the predefined accuracy, which is a hyperparameter that can be intuitively selected. The computation of the minimum required number of kernels is based on the frequency content of the demonstrated motion. The learning procedure essentially consists of the sampling of the demonstrated trajectory. The approach is validated through simulations and experiments with the KUKA LWR4+ robot, which show that utilizing the automatically calculated number of basis functions, the pre-defined accuracy is achieved by the proposed DMP model.