Reinforcement learning has produced capable controllers across a broad range of legged-robot tasks, but a subset of these tasks fail to converge under standard training: those for which most exploration trajectories terminate before producing useful gradient signal. To address such tasks we introduce the \emph{Actuator Dynamics Curriculum}, a procedure that initializes joint stiffness at a high value and anneals it toward the system-identified value as completed episode lengths grow. Using a cart-pole system as a representative example, we show that higher closed-loop joint natural frequency under critical damping enlarges the viability kernel of the underlying Markov Decision Process, increasing the fraction of initial states from which the task is feasible. We validate the kernel monotonicity on the cart-pole and apply the curriculum to a quadrupedal-to-handstand transition on the Boston Dynamics Spot, a narrow-viability task where training under fixed identified stiffness plateaus at a policy that never completes the transition. The trained policy executes the transition in simulation across 10 seeds and transfers to hardware. More broadly, our results suggest that simulated actuator dynamics is a useful axis along which to design curricula for tasks in which exploration is bottlenecked by termination conditions rather than by reward signal.
Quadrupedal locomotion plays a critical role in enabling agile, versatile movement across complex terrains. Understanding and estimating the underlying physical dynamics are essential for achieving efficient and stable quadrupedal locomotion. We propose a novel training framework for quadrupedal locomotion that enables the Control Policy to understand and reason about physical dynamics. In simulation, we concurrently train an Intrinsic Dynamics (ID) Head that learns state-to-torque dynamics alongside the Control Policy, and we define a dynamics reward enabled by the ID Head that encourages the Policy toward more predictable dynamical behavior. We also provide a mechanism to tune the learned dynamics in the resulting Policy by controlling the training coefficients of the ID Head. Our simulation experiments show that this mechanism drives convergence to better optima across a wide range of standard quadrupedal locomotion rewards, yielding more efficient and smoother policies. Our real-robot experiments demonstrate sim-to-real transfer of these improvements, with significant gains in torque efficiency (16.8%), action rate (18.6%), and mechanical power (12.8%), while improving safe torque occupancy by 6.4%.
Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL). These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walking-trot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO). We instantiate the approach on Google's Barkour quadruped robot in MuJoCo XLA (MJX). We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website: https://stl-locomotion.github.io/.
Learning dynamic whole-body motions for legged robots through reinforcement learning (RL) remains challenging due to the high risk of failure, which makes efficient exploration difficult and often leads to unstable learning. In this paper, we propose External Force Guided Curriculum Learning (EFGCL), a guided RL approach based on the principle of physical guidance, in which external assistive forces are introduced during training. Inspired by spotting in artistic gymnastics, EFGCL enables agents to physically experience successful motion executions without relying on task-specific reward shaping or reference trajectories. Experiments on a quadrupedal robot performing Jump, Backflip, and Lateral-Flip tasks demonstrate that EFGCL accelerates learning of the Jump task by approximately a factor of two and enables the acquisition of complex whole body motions that conventional RL methods fail to learn. We further show that the learned policies can be deployed on real robot, reproducing motions consistent with those observed in simulation. These results indicate that physically guided exploration, which allows agents to experience success early in training, is an effective and general strategy for improving learning efficiency in dynamic whole-body motion tasks.