基于共形预测与收缩分析的不确定地形上概率安全双足导航
Probabilistically-Safe Bipedal Navigation over Uncertain Terrain via Conformal Prediction and Contraction Analysis
AI总结：
针对不确定地形上的双足导航，提出结合共形预测与收缩分析的MPC框架，实现概率安全与目标可达，并通过Digit机器人仿真验证。
摘要：
我们通过开发概率上安全的规划与控制策略，解决双足机器人在粗糙地形上行走的挑战，这些策略在地形不确定性下确保动态可行性和质心鲁棒性。具体而言，我们为一个双足机器人提出了一种具有指定安全置信水平的高层模型预测控制（MPC）导航框架，该框架（i）能够在具有不确定高程的地形图中安全地向期望目标位置行进，并且（ii）将不确定性界限正式纳入运动控制的质心动力学中。为了对粗糙地形进行建模，我们采用高斯过程（GP）回归来估计高程图，并利用共形预测（CP）构建校准的置信区间，以捕捉真实地形高程。在此基础上，我们制定了基于收缩的可达管，明确考虑地形不确定性，确保状态收敛和管不变性。此外，我们为降阶线性倒立摆模型（LIPM）引入了一种基于收缩的飞轮扭矩控制律，该控制律稳定了围绕质心（CoM）的角动量。该公式提供了概率安全性和目标可达性保证。对于给定的置信水平，我们通过证明实际CoM相空间轨迹与高层规划器指定的期望轨迹的指数稳定性，建立了所提出的扭矩控制律的前向不变性。最后，我们通过MuJoCo中Digit双足机器人的基于物理的仿真来评估我们规划框架的有效性。
英文摘要：
We address the challenge of enabling bipedal robots to traverse rough terrain by developing probabilistically safe planning and control strategies that ensure dynamic feasibility and centroidal robustness under terrain uncertainty. Specifically, we propose a high-level Model Predictive Control (MPC) navigation framework for a bipedal robot with a specified confidence level of safety that (i) enables safe traversal toward a desired goal location across a terrain map with uncertain elevations, and (ii) formally incorporates uncertainty bounds into the centroidal dynamics of locomotion control. To model the rough terrain, we employ Gaussian Process (GP) regression to estimate elevation maps and leverage Conformal Prediction (CP) to construct calibrated confidence intervals that capture the true terrain elevation. Building on this, we formulate contraction-based reachable tubes that explicitly account for terrain uncertainty, ensuring state convergence and tube invariance. In addition, we introduce a contraction-based flywheel torque control law for the reduced-order Linear Inverted Pendulum Model (LIPM), which stabilizes the angular momentum about the center-of-mass (CoM). This formulation provides both probabilistic safety and goal reachability guarantees. For a given confidence level, we establish the forward invariance of the proposed torque control law by demonstrating exponential stabilization of the actual CoM phase-space trajectory and the desired trajectory prescribed by the high-level planner. Finally, we evaluate the effectiveness of our planning framework through physics-based simulations of the Digit bipedal robot in MuJoCo.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
