A core strength of Model Predictive Control (MPC) for quadrupedal locomotion has been its ability to enforce constraints and provide interpretability of the sequence of commands over the horizon. However, despite being able to plan, MPC struggles to scale with task complexity, often failing to achieve robust behavior on rapidly changing surfaces. On the other hand, model-free Reinforcement Learning (RL) methods have outperformed MPC on multiple terrains, showing emergent motions but inherently lack any ability to handle constraints or perform planning. To address these limitations, we propose a framework that integrates proprioceptive planning with RL, allowing for agile and safe locomotion behaviors through the horizon. Inspired by MPC, we incorporate an internal model that includes a velocity estimator and a Dreamer module. During training, the framework learns an expert policy and an internal model that are co-dependent, facilitating exploration for improved locomotion behaviors. During deployment, the Dreamer module solves an infinite-horizon MPC problem, adapting actions and velocity commands to respect the constraints. We validate the robustness of our training framework through ablation studies on internal model components and demonstrate improved robustness to training noise. Finally, we evaluate our approach across multi-terrain scenarios in both simulation and hardware.

This work presents a simple linear policy for direct force control for quadrupedal robot locomotion. The motivation is that force control is essential for highly dynamic and agile motions. We learn a linear policy to generate end-foot trajectory parameters and a centroidal wrench, which is then distributed among the legs based on the foot contact information using a quadratic program (QP) to get the desired ground reaction forces. Unlike the majority of the existing works that use complex nonlinear function approximators to represent the RL policy or model predictive control (MPC) methods with many optimization variables in the order of hundred, our controller uses a simple linear function approximator to represent policy along with only a twelve variable QP for the force distribution. A centroidal dynamics-based MPC method is used to generate reference trajectory data, and then the linear policy is trained using imitation learning to minimize the deviations from the reference trajectory. We demonstrate this compute-efficient controller on our robot Stoch3 in simulation and real-world experiments on indoor and outdoor terrains with push recovery.