In this work, we propose a trajectory generation method for robotic systems with contact kinematics and force constraints based on optimal control and reachability analysis tools. Normally, the dynamics and constraints of a contact-constrained robot are nonlinear and coupled to each other. Instead of linearizing the model and constraints, we solve the optimal control problem directly to obtain feasible state trajectories and their corresponding control inputs. A tractable optimal control problem is formulated and subsequently addressed by dual approaches, which rely on sampling-based dynamic programming and rigorous reachability analysis tools. In particular, a sampling-based method together with a Partially Observable Markov Decision Process solution approach are used to break down the end-to-end trajectory generation problem by generating a sequence of subregions that the system’s trajectory will have to pass through to reach its final destination. The distinctive characteristic of the proposed trajectory optimization algorithm is its ability to handle the intricate contact constraints, coupled with the system dynamics, in a computationally efficient way. We validate our method using extensive numerical simulations with two legged robots.

在这项工作中，我们提出了一种基于最优控制和可达性分析工具的具有接触运动学和力约束的机器人系统轨迹生成方法。通常，接触受限机器人的动力学和约束是非线性的，并且相互耦合。我们无需线性化模型和约束，而是直接解决最优控制问题，以获得可行的状态轨迹及其相应的控制输入。提出了一个易于处理的最优控制问题，并随后通过双重方法解决，该方法依赖于基于采样的动态规划和严格的可达性分析工具。特别是，基于采样的方法与部分可观察的马尔可夫决策过程解决方案方法一起使用，通过生成系统轨迹必须到达其最终目的地的一系列子区域来解决端到端轨迹生成问题。所提出的轨迹优化算法的显着特征是其以计算有效的方式处理复杂的接触约束以及系统动力学的能力。我们使用带有两个腿的机器人的大量数值模拟来验证我们的方法。以高效的计算方式与系统动力学相结合。我们使用带有两个腿的机器人的大量数值模拟来验证我们的方法。以高效的计算方式与系统动力学相结合。我们使用带有两个腿的机器人的大量数值模拟来验证我们的方法。