Learning nonlinear multi-variate motion dynamics for real-time position and orientation control of robotic manipulators

Abstract

Abstract-We present a generic framework that allows learning non-linear dynamics of motion in manipulation tasks and generating dynamical laws for control of position and orientation. This work follows a recent trend in Programming by Demonstration in which the dynamics of an arm motion is learned: position and orientation control are learned as multivariate dynamical systems to preserve correlation within the signals. The strength of the method is three-fold: i) it extracts dynamical control laws from demonstrations, and subsequently provides concurrent smooth control of both position and orientation; ii) it allows to generalize a motion to unseen context; iii) it guarantees on-line adaptation of the motion in the face of spatial and temporal perturbations. The method is validated to control a four degree of freedom humanoid arm and an industrial six degree of freedom robotic arm.

Coupled dynamical system based arm–hand grasping model for learning fast adaptation strategies

“…This offers great robustness in the face of perturbations, as a new desired trajectory can be recomputed on the fly with no need to re-plan [5][6][7]. We follow this trend and extend our previous works [8,9] on learning a motor control law using time-invariant dynamical systems. Such a control law generates trajectories that are asymptotically stable at a single attractor.…”

“…Figure 6 shows the streamlines of this system for two different α values in order to visualize the global behavior of trajectories evolving under the CDS model. At this point, it is important to distinguish our approach from the single GMM approach of [8] mentioned in section 3.2. Figure 7 shows a comparison of the CDS trajectories with those obtained using the single GMM approach, where the coupling is only implicit.…”

“…The regression assumes a model for the underlying process and learns its parameters via machine learning techniques. Subsequently, multiple works under the PbD framework [2,8,47] have shown that this problem can be handled elegantly by using the dynamical systems (DS) approach. Using DS to represent motion removes the explicit time dependency from the model.…”

“…The resulting mixtures for each of the models is shown in Figure 3. For reproducing the task, instead of using the earlier approach of [8] where the system evolves under the velocities computed as E (ξ x ;ξ f ) |(ξ x ; ξ f ) , we proceed as in Algorithm 1. perturbation in ξ x creates an effect in ξ f , i.e., generating a negative velocity, the magnitude of which is tunable using the α parameter. This change is brought due to the need of tracking the inferred ξ f values i.e.ξ f , at all ξ x .ξ f represents the expected value of ξ f given ξ x as seen during the demonstrations.…”

Estimating the non-linear dynamics of free-flying objects

“…where N (ζ |µ k , Σ k ) is a Gaussian distribution with mean µ k and covariance matrix Σ k ; h k (ζ ) gives a measure of the influence of the kth Gaussian in generating the data point ζ ; see [57] for details.…”