Mixed-type decision-making is ubiquitously required in robotic systems and has attracted significant research interests. Examples include, but not limited to, the integrated task and motion planning and optimal control of hybrid systems involving both continuous and discrete dynamic behaviors. For decision-making of robotic systems to improve operational efficiency, safety, and/or mission success rate, they involve both discrete variables representing task allocation or transitions between discrete modes and continuous variables representing trajectories of the planned motion or states governed by differential equations. This paper formulates a class of mixed-type decision-making problems with polynomial objective and constraints as quadratically constrained quadratic programming (QCQP) problems and a nonconvex optimization method based on alternating direction method of multipliers is proposed to solve the QCQP. The proposed optimization method consists of three sequential subproblems, all of which admit closed-form solutions. Moreover, convergence proof of the optimization algorithm is provided. Two representative problems, traveling salesman with obstacle avoidance and rendezvous and docking of a charging station with distinct phase constraints, are described and solved via the proposed method. Numerical simulations as well as experimental verification of both problems are presented and compared with a state-of-art method to validate the effectiveness, efficacy and robustness of the nonconvex optimization method.

中文翻译：

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机器人系统混合型决策的统一表述和非凸优化方法


机器人系统普遍需要混合型决策，并引起了人们的广泛研究兴趣。示例包括但不限于涉及连续和离散动态行为的混合系统的集成任务和运动规划以及最优控制。对于机器人系统的决策以提高操作效率、安全性和/或任务成功率，它们涉及表示任务分配或离散模式之间的转换的离散变量和表示计划运动的轨迹或由微分方程控制的状态的连续变量。将一类具有多项式目标和约束的混合型决策问题表述为二次约束二次规划(QCQP)问题，并提出一种基于乘子交替方向法的非凸优化方法来求解QCQP。所提出的优化方法由三个连续的子问题组成，所有子问题都允许封闭式解。此外，还提供了优化算法的收敛性证明。通过所提出的方法描述并解决了两个代表性问题，即旅行商的避障问题和具有不同相位约束的充电站的交会对接问题。对这两个问题进行了数值模拟和实验验证，并与最先进的方法进行了比较，以验证非凸优化方法的有效性、功效和鲁棒性。