Developing feasible body trajectories for legged systems on arbitrary terrains is a challenging task. In this paper, we present a paradigm that allows to design feasible Center of Mass (CoM) and body trajectories in an efficient manner. In our previous work [1], we introduced the notion of the 2D feasible region, where static balance and the satisfaction of joint torque limits were guaranteed, whenever the projection of the CoM lied inside the proposed admissible region. In this work we propose a general formulation of the improved feasible region that guarantees dynamic balance alongside the satisfaction of both joint-torque and kinematic limits in an efficient manner. To incorporate the feasibility of the kinematic limits, we introduce an algorithm that computes the reachable region of the CoM. Furthermore, we propose an efficient planning strategy that utilizes the improved feasible region to design feasible CoM and body orientation trajectories. Finally, we validate the capabilities of the improved feasible region and the effectiveness of the proposed planning strategy, using simulations and experiments on the 90 kg Hydraulically actuated Quadruped (HyQ) and the 21 kg Aliengo robots.

翻译：为足式系统在任意地形上设计可行的身体轨迹是一项具有挑战性的任务。本文提出了一种能够高效设计可行质心和身体轨迹的范式。在先前工作[1]中，我们引入了二维可行区域的概念，当质心投影位于所提出的可行区域内时，可保证静态平衡并满足关节力矩极限。本研究提出了一种改进可行区域的通用公式，该公式能够高效地保证动态平衡，同时满足关节力矩和运动学极限。为纳入运动学极限的可行性，我们引入了一种计算质心可达区域的算法。此外，我们提出了一种高效的规划策略，利用改进的可行区域来设计可行的质心和身体朝向轨迹。最后，通过在90公斤液压驱动四足机器人（HyQ）和21公斤Aliengo机器人上的仿真与实验，验证了改进可行区域的能力及所提规划策略的有效性。