Soft robots have the potential to interact with sensitive environments and perform complex tasks effectively. However, motion plans and trajectories for soft manipulators are challenging to calculate due to their deformable nature and nonlinear dynamics. This article introduces a fast real-time trajectory generation approach for soft robot manipulators, which creates dynamically-feasible motions for arbitrary kinematically-feasible paths of the robot's end effector. Our insight is that piecewise constant curvature (PCC) dynamics models of soft robots can be differentially flat, therefore control inputs can be calculated algebraically rather than through a nonlinear differential equation. We prove this flatness under certain conditions, with the curvatures of the robot as the flat outputs. Our two-step trajectory generation approach uses an inverse kinematics procedure to calculate a motion plan of robot curvatures per end-effector position, then, our flatness diffeomorphism generates corresponding control inputs that respect velocity. We validate our approach through simulations of our representative soft robot manipulator along three different trajectories, demonstrating a margin of 23x faster than real-time at a frequency of 100 Hz. This approach could allow fast verifiable replanning of soft robots' motions in safety-critical physical environments, crucial for deployment in the real world.

翻译：软体机器人具备与敏感环境交互并有效执行复杂任务的潜力。然而，由于其可变形特性和非线性动力学特性，软体机械臂的运动规划与轨迹计算具有挑战性。本文提出一种用于软体机器人机械臂的快速实时轨迹生成方法，该方法可为机器人末端执行器的任意运动学可行路径生成动力学可行的运动。我们的核心洞见在于：软体机器人的分段常曲率（PCC）动力学模型可能具有微分平坦性，因此控制输入可通过代数运算而非非线性微分方程求解。我们在特定条件下证明了该平坦性，并以机器人曲率作为平坦输出。我们的两步轨迹生成方法首先通过逆运动学程序计算各末端执行器位置对应的机器人曲率运动规划，随后利用平坦微分同胚生成满足速度约束的对应控制输入。通过对代表性软体机器人机械臂沿三条不同轨迹的仿真实验，我们验证了该方法在100 Hz频率下可实现比实时快23倍的运算裕度。该方法有望在安全关键物理环境中实现软体机器人运动的快速可验证重规划，这对实际应用部署至关重要。