Trajectory Optimization and Force Control with Modified Dynamic Movement Primitives under Curved Surface Constraints

A model predictive obstacle avoidance method based on dynamic motion primitives and a Kalman filter

“…where p(x, v) is the negative gradient of the potential field [27] and 𝜆 is a constant that indicates the strength of the entire field [10,28]. The potential field depends on the relative position and velocity of the end effector with respect to the obstacle.…”

“…Based on this consideration, a repulsive potential field is established around the obstacles, and the DMP method is combined with this potential field. We add a perturbation term $$$ \mathbf{p}\left(\mathbf{x},\mathbf{v}\right) $$$ to the attraction system Equation (): $$$$ {\displaystyle \begin{array}{cc}\hfill \tau \dot{\mathbf{v}}=& \mathbf{K}\left(\mathbf{g}-\mathbf{x}\right)-\mathbf{Dv}+\mathit{\operatorname{diag}}\left(\mathbf{g}-{\mathbf{x}}_0\right)\mathbf{f}+\lambda \mathbf{p}\left(\mathbf{x},\mathbf{v}\right),\hfill \\ {}\hfill \tau \dot{\mathbf{x}}=& \mathbf{v},\hfill \end{array}}, $$$$ where $$$ \mathbf{p}\left(\mathbf{x},\mathbf{v}\right) $$$ is the negative gradient of the potential field [27] and $$$ \lambda $$$ is a constant that indicates the strength of the entire field [10, 28]. The potential field depends on the relative position and velocity of the end effector with respect to the obstacle.…”

Motion optimization for safe robot–environment interaction with force constraints

“…It is worth to note that the such force transformation system has been fully developed in the past years to provide more compromise format such as adding internal force constraint term to achieve the obstacle avoidance [26], plussing a force coupling parameter to enable the motion satisfy the curved surface constraint [27], and considering a bias term to each kernel [33], etc. In these ways, the DMPs motions can be encoded with a specific smooth path by modulating a desired 𝜔 i , h i , and c i .…”

“…Inspired by the state constraints in robotic control point of view, many researchers brought forward a solution determining the coupling terms to obtain a constraint motion for specific situation. In reference [27], an accelerating coupling term is deduced to improve the DMPs structure while generalizing a motion from flat to curve surface. In reference [28], a safety interaction margin is designed in terms of the convex shape for the obstacle avoidance.…”

A review on manipulation skill acquisition through teleoperation‐based learning from demonstration

“…Thus, it is hard to model the correlation between the sensory value and the states of robots. In addition, the original DMP cannot achieve the force control of robots for contact tasks, such as assembly [54]. Therefore, since the original DMP was proposed, a variety of modified DMPs were proposed to tackle with limitations as mentioned earlier.…”