Footstep planning in various three-dimensional environments is formulated as an optimization problem, which is solved using a particle swarm optimi-zation. The objective function for optimization is designed to achieve real-time footstep planning considering arrival at the goal with effective not only foot placements but also walking periods, kinematic constraints: obstacle avoidance and hardware limitations, and dynamic constraints for the bipedal dynamics: stability while walking and feasibility of footsteps in a walking pattern generator. Specifically, optimization objectives are to minimize remaining distance to the goal, lateral movement, rotational movement, and walking period variation. Three penalties are also consid-ered depending on the situations. The first penalty is for obstacle collision avoidance along with prevention of unstable walking due to excessive footstep height variation. The second penalty is for walking satisfying stable zero-moment point condition along with the foot collision avoidance. The third penalty is for feasible footstep planning in a walking pattern generator. Any approxi-mation or precomputation is not required for the proposed footstep planning method. The validity of the proposed method is verified through experiments in various 3-D environments with static and dynamic obstacles.

中文翻译：

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使用粒子群算法的三维环境中双足机器人的实时可行足迹规划

各种三维环境中的足迹计划被表述为一个优化问题，可以使用粒子群优化来解决。优化的目标函数旨在实现实时脚步计划，考虑到目标的到达，不仅有效地放置脚步，而且还有效步行，运动学约束：避障和硬件限制，以及双足动力的动态约束：步行时的稳定性行走模式发生器中足迹的可行性和可行性。具体来说，优化目标是使与目标的剩余距离，横向运动，旋转运动和步行时间变化最小化。根据情况还考虑了三项处罚。首要的惩罚是避免障碍物碰撞以及防止由于过度的脚步高度变化而导致的不稳定步行。第二个惩罚是步行时要满足稳定的零矩点条件，同时还要避免避开脚部碰撞。第三个惩罚是在步行模式发生器中可行的脚步规划。建议的足迹计划方法不需要任何近似或预计算。通过在具有静态和动态障碍的各种3-D环境中进行实验，验证了该方法的有效性。建议的足迹计划方法不需要任何近似或预计算。通过在具有静态和动态障碍的各种3-D环境中进行实验，验证了该方法的有效性。建议的足迹计划方法不需要任何近似或预计算。通过在具有静态和动态障碍的各种3-D环境中进行实验，验证了该方法的有效性。