A Real-Time Solver For Time-Optimal Control Of Omnidirectional Robots with Bounded Acceleration

We are interested in the problem of time-optimal control of omnidirectional robots with bounded acceleration (TOC-ORBA). While there exist approximate solutions for such robots, and exact solutions with unbounded acceleration, exact solvers to the TOC-ORBA problem have remained elusive until now. In this paper, we present a real-time solver for true time-optimal control of omnidirectional robots with bounded acceleration. We first derive the general parameterized form of the solution to the TOC-ORBA problem by application of Pontryagin's maximum principle. We then frame the boundary value problem of TOC-ORBA as an optimization problem over the parametrized control space. To overcome local minima and poor initial guesses to the optimization problem, we introduce a two-stage optimal control solver (TSOCS): The first stage computes an upper bound to the total time for the TOC-ORBA problem and holds the time constant while optimizing the parameters of the trajectory to approach the boundary value conditions. The second stage uses the parameters found by the first stage, and relaxes the constraint on the total time to solve for the parameters of the complete TOC-ORBA problem. We further implement TSOCS as a closed loop controller to overcome actuation errors on real robots in real-time. We empirically demonstrate the effectiveness of TSOCS in simulation and on real robots, showing that 1) it runs in real time, generating solutions in less than 0.5ms on average; 2) it generates faster trajectories compared to an approximate solver; and 3) it is able to solve TOC-ORBA problems with non-zero final velocities that were previously unsolvable in real-time

Velocity constrained trajectory generation for a collinear Mecanum wheeled robot

While much research has been conducted into the generation of smooth trajectories for underactuated unstable aerial vehicles such as quadrotors, less attention has been paid to the application of the same techniques to ground based omnidirectional dynamically balancing robots. These systems have more control authority over their linear accelerations than aerial vehicles, meaning trajectory smoothness is less of a critical design parameter. However, when operating in indoor environments these systems must often adhere to relatively low velocity constraints, resulting in very conservative trajectories when enforced using existing trajectory optimisation methods. This paper makes two contributions; this gap is bridged by the extension of these existing methods to create a fast velocity constrained trajectory planner, with trajectory timing characteristics derived from the optimal minimum-time solution of a simplified acceleration and velocity constrained model. Next, a differentially flat model of an omnidirectional balancing robot utilizing a collinear Mecanum drive is derived, which is used to allow an experimental prototype of this configuration to smoothly follow these velocity constrained trajectories

A Convex Approach to Path Tracking with Obstacle Avoidance for Pseudo-Omnidirectional Vehicles

This report addresses the related problems of trajectory generation and time-optimal path tracking with online obstacle avoidance. We consider the class of four-wheeled vehicles with independent steering and driving on each wheel, also referred to as pseudo-omnidirectional vehicles. Appropriate approximations of the dynamic model enable a convex reformulation of the path-tracking problem. Using the precomputed trajectories together with model predictive control that utilizes feedback from the estimated global pose, provides robustness to model uncertainty and disturbances. The considered approach also incorporates avoidance of a priori unknown moving obstacles by local online replanning. We verify the approach by successful execution on a pseudo-omnidirectional mobile robot, and compare it to an existing algorithm. The result is a significant decrease in the time for completing the desired path. In addition, the method allows a smooth velocity trajectory while avoiding intermittent stops in the path execution

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available