Dynamically Consistent Online Adaptation of Fast Motions for Robotic Manipulators

Abstract

Abstract-The planning and execution of real-world robotic tasks largely depend on the ability to generate feasible motions online in response to changing environment conditions or goals. A spline deformation method is able to modify a given trajectory so that it matches the new boundary conditions, e.g. on positions, velocities, accelerations, etc. At the same time, the deformed motion preserves velocity, acceleration, jerk or higher derivatives of motion profile of precalculated trajectory. The deformed motion possessing such properties can be expressed by translation of original trajectory and spline interpolation. This spline decomposition considerably reduces the computational complexity and allows the real-time execution. Formal feasibility guarantees are provided for the deformed trajectory and for the resulting torques. These guarantees are based on the special properties of Bernstein polynomials used for the deformation and on the structure of the chosen computed torque control scheme. The approach is experimentally evaluated in a number of planar volleyball experiments using 3-DoF robots and human participants.

Shape-Preserving and Reactive Adaptation of Robot End-Effector Trajectories

“…Compared to other trajectory deformation methods [10], [14], [13], the shape-preserving trajectory generator has no issues generalizing in different regions of the task space since a coordinate-free norm related to the shape deformation is minimized instead of a distance norm in Cartesian space. Another advantage is the flexibility with which trajectory constraints can be specified or not.…”

“…The choice of distance metric can be further generalized to a problem over a Hilbert space [13]. Instead of the trajectory distance, the motion profile (or its derivatives) can also be preserved as the characteristic motion features [14]. This paper's method, based on [3], fits in the latter trajectory optimization category, but instead of using a norm in Cartesian space, we try to minimize a norm based on a coordinate-invariant description of the shape allowing for better generalization in different regions of the state space.…”

Intelligent automation of dental material analysis using robotic arm with Jerk optimized trajectory

“…Local derivative properties of original trajectory are encoded with the differential Laplace Beltrami operator. Following Pekarovskiy et al (2018), we use local derivatives of motion profile that are calculated for each sampling point i through the finite difference. The velocity and the acceleration, and jerk along trajectory are derived as follows:…”

Generalizing demonstrated motion trajectories using coordinate-free shape descriptors

“…In the objective function a cost term is introduced to preserve similarity with the original demonstration. For example in [32], this cost is the deviation of the motion profile (velocity, acceleration or jerk) of the generated trajectory to the motion profile of the original trajectory. In human motor control, the jerk is often minimized along the trajectory in order to obtain the typical bell-shaped motion profile with which humans execute their motions.…”