Fast Risk-Sensitive Model Predictive Control for Systems with Time-Series Forecasting Uncertainties

Abstract

This paper proposes a novel control framework for agile and robust bipedal locomotion, addressing model discrepancies between full-body and reduced-order models. Specifically, assumptions such as constant centroidal inertia have introduced significant challenges and limitations in locomotion tasks. To enhance the agility and versatility of fullbody humanoid robots, we formalize a Model Predictive Control (MPC) problem that accounts for the variable centroidal inertia of humanoid robots within a convex optimization framework, ensuring computational efficiency for real-time operations. In this formulation, we incorporate a centroidal inertia network designed to predict the variable centroidal inertia over the MPC horizon, taking into account the swing foot trajectories-an aspect often overlooked in ROM-based MPC frameworks. Moreover, we enhance the performance and stability of locomotion behaviors by synergizing the MPC-based approach with whole-body control (WBC). The effectiveness of our proposed framework is validated through simulations using our fullbody humanoid robot, DRACO 3 [1], demonstrating dynamic behaviors.

Autonomous Navigation of AGVs in Unknown Cluttered Environments: Log-MPPI Control Strategy

“…It is worth emphasizing that a similar form of (32), along with its derivation, can be found in [8]. However, the presented derivation process in [8] is brief and lacks detailed explanations and clarifications.…”

“…We then apply the underlying non-linear dynamics expressed in (9) to the sigma points, which can be merged into a single vector using (10). Finally, we use the resulting sigma points X 1 at k = 1 to estimate the first and second moments, namely x1 and Σ 1 , of the propagated state vector x 1 by applying (8). This propagation process is repeated until k = N − 1, resulting in a sequence of state vectors denoted as X k N i=0 , which represent the n σ propagated sigma points.…”

“…On the other hand, if γ > 0, the penalty matrix decreases as the uncertainty level increases. Additionally, when γ = 0, the penalty remains constant and equal to the weighting matrix Q, regardless of the level of the uncertainty [8]. More in-depth analysis of how the U-MPPI performance is influenced by the sign of γ is discussed in Section V-A1.…”

Risk of Stochastic Systems for Temporal Logic Specifications

“…A similar idea is followed for the risk constrained minimum mean squared error estimator in [37]. Risk-aware model predictive control was considered in [29,76], while [17,73] present data-driven and distributionally robust model predictive controllers. Risk-aware control barrier functions for safe control synthesis were proposed in [2], while [58] demonstrates the use of risk in sampling-based planning.…”

STL Robustness Risk over Discrete-Time Stochastic Processes

“…More recently, there has been an interest to also apply such risk measures in robotics and control applications [25]. Riskaware control and estimation frameworks have recently appeared in [26][27][28][29][30][31][32][33] using various forms of risk. We remark that these frameworks are orthogonal to our work as they present design tools while we provide a generic framework for quantifying the risk of complex system specifications expressed in STL.…”