Reinforcement learning (RL) is a powerful and convenient tool to modernize controller design. In this work, we study the zero-shot transfer of RL-based control policies from simulation to hardware for cart-pole swing-up and stabilization. The two policies are trained independently, and the handoff is implemented in Simulink via switching logic. We apply a first-order action smoothing filter to prevent hardware damage from high-frequency oscillatory actuation. Pairing this bandwidth-aware filtering with sensitivity-guided domain randomization (DR) and a simple linear curriculum learning (CL) schedule, we obtain a swing-up policy that in all of our experiments injects sufficient energy for handoff into the stabilizer's region of attraction. The stabilization policy rejects disturbances within the tested range, and the swing-up policy can re-engage after larger perturbations and restores the pendulum to the inverted position.
The cart-pole swing-up is a canonical benchmark for nonlinear control of underactuated systems, yet an end-to-end guarantee linking the global swing-up maneuver to the local stabilizer is seldom formalized. We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium from a compact set of initial conditions. The swing-up law is derived from an energy-error Lyapunov function; canceling the autonomous conservative term yields a strictly sign-definite Lyapunov derivative, and convergence follows from LaSalle's invariance principle. We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence. For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition. Numerical simulations corroborate the theoretical analysis.
Reinforcement learning (RL) has become the de facto method for achieving locomotion on humanoid robots in practice, yet stability analysis of the corresponding control policies is lacking. Recent work has attempted to merge control theoretic ideas with reinforcement learning through control guided learning. A notable example of this is the use of a control Lyapunov function (CLF) to synthesize the reinforcement learning rewards, a technique known as CLF-RL, which has shown practical success. This paper investigates the stability properties of optimal controllers using CLF-RL with the goal of bridging experimentally observed stability with theoretical guarantees. The RL problem is viewed as an optimal control problem and exponential stability is proven in both continuous and discrete time using both core CLF reward terms and the additional terms used in practice. The theoretical bounds are numerically verified on systems such as the double integrator and cart-pole. Finally, the CLF guided rewards are implemented for a walking humanoid robot to generate stable periodic orbits.
Robots trained on real world data tend to be imprecise, slow, and brittle to perturbations. Improving these policies with reinforcement learning (RL) is an appealing alternative, but this process often requires expensive training in the real world. Performing policy improvement in simulation instead provides a far cheaper alternative, but unconstrained RL in simulation can exploit contact and dynamics mismatches, resulting in unsafe behaviors that do not transfer to hardware. Common forms of regularization can furthermore limit improvement by overconstraining to an imperfect behavior prior. In this work, we propose Support-Constrained Off-Domain REinforcement (SCORE), a real-to-sim-to-real framework that constrains RL in simulation to the support of a generative policy pretrained on real data. We instantiate this constraint through flow steering, restricting SCORE to actions the base policy can already produce, which ensures transferable behaviors while maximizing policy improvement. Improving a policy with SCORE requires minimal effort: it learns from sparse rewards, avoids distillation, and leaves the base policy untouched. Across eight real-world dexterous multi-fingered robotic manipulation tasks, SCORE improves average success rate from 37.8% to 89.9%, compared to 59.5% for the best baseline, and reaches success in 36.8% fewer steps than the base policy. Ultimately, through extensive experiments and ablations, we show that simulation can substantially improve real-world manipulation policies when policy optimization is appropriately constrained, introducing a new paradigm for real-to-sim-to-real policy improvement. Videos and code are available at https://weirdlabuw.github.io/score/.