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.

The average reward criterion is relatively less studied as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this work, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We first show asymptotic convergence analysis using the ODE-based method. Subsequently, we provide a finite time analysis of the resulting stochastic approximation scheme with linear function approximator and obtain an $\epsilon$-optimal stationary policy with a sample complexity of $\Omega(\epsilon^{-2.5})$. We compare the average reward performance of our proposed ARO-DDPG algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo-based environments.