MPPI-VS: Sampling-Based Model Predictive Control Strategy for Constrained Image-Based and Position-Based Visual Servoing

Abstract

In this paper, we open up new avenues for visual servoing systems built upon the Path Integral (PI) optimal control theory, in which the non-linear partial differential equation (PDE) can be transformed into an expectation over all possible trajectories using the Feynman-Kac (FK) lemma. More precisely, we propose an MPPI-VS control strategy, a real-time and inversion-free control strategy on the basis of samplingbased model predictive control (namely, Model Predictive Path Integral (MPPI) control) algorithm, for both image-based, 3D point, and position-based visual servoing techniques, taking into account the system constraints (such as visibility, 3D, and control constraints) and parametric uncertainties associated with the robot and camera models as well as measurement noise. Contrary to classical visual servoing control schemes, our control strategy directly utilizes the approximation of the interaction matrix, without the need for estimating the interaction matrix inversion or performing the pseudo-inversion. We validate the MPPI-VS control strategy as well as the classical control schemes on a 6-DoF Cartesian robot with an eye-in-hand camera based on the utilization of four points in the image plane as visual features.To better assess and demonstrate the robustness and potential advantages of our proposed control strategy compared to classical schemes, intensive simulations under various operating conditions are carried out and then discussed. The obtained results demonstrate the effectiveness and capability of the proposed scheme in coping easily with the system constraints, as well as its robustness in the presence of large errors in camera parameters and measurements.

Autonomous Navigation of AGVs in Unknown Cluttered Environments: Log-MPPI Control Strategy

“…Therefore, we have chosen γ = 1 to maintain this trade-off and strike a balance between task completion and collision avoidance. On the other hand, we believe that assigning negative values to γ in applications such as autonomous racing [28] and visual servoing [14] could enhance the performance of U-MPPI. In such tasks, it is crucial to prioritize forcing the current state to reach its desired state, which can be achieved by assigning a higher penalty coefficients matrix Q rs .…”

“…Such a method solves the stochastic optimal control problem in a receding-horizon control setting by: (i) leveraging Monte Carlo simulation to rollout real-time simulated trajectories propagated from the system dynamics, (ii) evaluating these trajectories, (iii) computing the optimal control sequence by taking the weighted average of the costs of the sampled trajectories, and (iv) applying the first control input to the system while using the remaining control sequence to warm-start the optimization in the next time-step, enabling the method to solve the optimization problem effectively [11]. MPPI stands out among alternative MPC methods due to its attractive features, such as being a sampling-based and derivative-free optimization method, not relying on assumptions or approximations of objective functions and system dynamics, being effective for highly dynamic systems, and benefiting from parallel sampling and the computational capabilities of Graphics Processing Units (GPUs) to achieve optimized and real-time performance [14]. 1 While MPPI has appealing characteristics, it may also pose challenges in practice.…”

Autonomous Navigation of AGVs in Unknown Cluttered Environments: log-MPPI Control Strategy

“…By Ito's formula, we can get the following computation for d B(t)e W1(t) : e W1(t) dB(t) + B(t)de W1(t) + d[B(t), e W1(t) ] = e W1(t) dB(t)+B(t) σ ln e W1(t) dB 1 (t)+κe W1(t) dt . (14) Thus, the sampling dynamics can be viewed as a modified one…”

“…Recently, MPPI or sampling-based MPC has been successfully applied to a wide variety of robotic applications, starting from aggressive driving [9], [10] and autonomous flight [1], [11] and ending with visual servoing [12] and reactive manipulation [13], showing outstanding performance in the presence of non-convex and discontinuous objectives, without adding any additional complexity to the optimization problem. Despite the attractive characteristics of MPPI [14], much like any sampling-based optimization method, it might generate an infeasible control sequence (i.e., infeasible trajectory) when the distributions of all sampled trajectories drawn from the system dynamics are unfortunately surrounding some infeasible region. This may inevitably lead to either violating the system constraints or increasing the risk of being trapped in local minima.…”