Sampling-based kinodynamic motion planners (SKMPs) are powerful in finding collision-free trajectories for high-dimensional systems under differential constraints. Time-informed set (TIS) can provide the heuristic search domain to accelerate their convergence to the time-optimal solution. However, existing TIS approximation methods suffer from the curse of dimensionality, computational burden, and limited system applicable scope, e.g., linear and polynomial nonlinear systems. To overcome these problems, we propose a method by leveraging deep learning technology, Koopman operator theory, and random set theory. Specifically, we propose a Deep Invertible Koopman operator with control U model named DIKU to predict states forward and backward over a long horizon by modifying the auxiliary network with an invertible neural network. A sampling-based approach, ASKU, performing reachability analysis for the DIKU is developed to approximate the TIS of nonlinear control systems online. Furthermore, we design an online time-informed SKMP using a direct sampling technique to draw uniform random samples in the TIS. Simulation experiment results demonstrate that our method outperforms other existing works, approximating TIS in near real-time and achieving superior planning performance in several time-optimal kinodynamic motion planning problems.

Learning-based methods have improved locomotion skills of quadruped robots through deep reinforcement learning. However, the sim-to-real gap and low sample efficiency still limit the skill transfer. To address this issue, we propose an efficient model-based learning framework that combines a world model with a policy network. We train a differentiable world model to predict future states and use it to directly supervise a Variational Autoencoder (VAE)-based policy network to imitate real animal behaviors. This significantly reduces the need for real interaction data and allows for rapid policy updates. We also develop a high-level network to track diverse commands and trajectories. Our simulated results show a tenfold sample efficiency increase compared to reinforcement learning methods such as PPO. In real-world testing, our policy achieves proficient command-following performance with only a two-minute data collection period and generalizes well to new speeds and paths.

In nature, legged animals have developed the ability to adapt to challenging terrains through perception, allowing them to plan safe body and foot trajectories in advance, which leads to safe and energy-efficient locomotion. Inspired by this observation, we present a novel approach to train a Deep Neural Network (DNN) policy that integrates proprioceptive and exteroceptive states with a parameterized trajectory generator for quadruped robots to traverse rough terrains. Our key idea is to use a DNN policy that can modify the parameters of the trajectory generator, such as foot height and frequency, to adapt to different terrains. To encourage the robot to step on safe regions and save energy consumption, we propose foot terrain reward and lifting foot height reward, respectively. By incorporating these rewards, our method can learn a safer and more efficient terrain-aware locomotion policy that can move a quadruped robot flexibly in any direction. To evaluate the effectiveness of our approach, we conduct simulation experiments on challenging terrains, including stairs, stepping stones, and poles. The simulation results demonstrate that our approach can successfully direct the robot to traverse such tough terrains in any direction. Furthermore, we validate our method on a real legged robot, which learns to traverse stepping stones with gaps over 25.5cm.

Recently reinforcement learning (RL) has emerged as a promising approach for quadrupedal locomotion, which can save the manual effort in conventional approaches such as designing skill-specific controllers. However, due to the complex nonlinear dynamics in quadrupedal robots and reward sparsity, it is still difficult for RL to learn effective gaits from scratch, especially in challenging tasks such as walking over the balance beam. To alleviate such difficulty, we propose a novel RL-based approach that contains an evolutionary foot trajectory generator. Unlike prior methods that use a fixed trajectory generator, the generator continually optimizes the shape of the output trajectory for the given task, providing diversified motion priors to guide the policy learning. The policy is trained with reinforcement learning to output residual control signals that fit different gaits. We then optimize the trajectory generator and policy network alternatively to stabilize the training and share the exploratory data to improve sample efficiency. As a result, our approach can solve a range of challenging tasks in simulation by learning from scratch, including walking on a balance beam and crawling through the cave. To further verify the effectiveness of our approach, we deploy the controller learned in the simulation on a 12-DoF quadrupedal robot, and it can successfully traverse challenging scenarios with efficient gaits.