A Set-Based Trajectory Planning Algorithm for a Network Controlled Skid-Steered Tracked Mobile Robot Subject to Skid and

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A Set-Based Trajectory Planning Algorithm for a Network Controlled Skid-Steered Tracked Mobile Robot Subject to Skid and Slip Phenomena Valerio Scordamaglia1 · Vito Antonio Nardi1 Received: 20 March 2020 / Accepted: 2 October 2020 © Springer Nature B.V. 2020

Abstract This paper aims to propose a solution to the feasible-trajectory planning problem for a tracked mobile robot subject to non-negligible skidding and slipping effects and whose control system, sensors and actuators are connected through a communication network. A trajectory is defined in terms of succession of linear segments with a prescribed crossing velocity and the trajectory feasibility is guaranteed in terms of sufficient conditions by recurring to set-based arguments formulated in terms of solution of semi-definite programming minimization problems (SDP) involving linear matrix inequalities (LMI) constraints. In order to show the effectiveness of proposed solution a campaign of numerical and experimental simulations involving the mobile robot V4 Jaguar by Dr.Robot is carried out. Keywords Optimal feasible trajectory planning · Robust invariant-set motion planning · Networked control systems · Skid-steered robot · Tracked mobile robot · Network controlled robot

1 Introduction In past years, many effort has been spent in terms of research activities to tackle the problem of trajectory planning for an autonomous mobile robot [1–4]. The solution of this problem plays a key role in many contexts [5–7] when the presence of different moving obstacle requires time-parametrized motion planning instead of simple geometrical paths [8]. An effective algorithm for the trajectory planning of a mobile robot must be able to find a path from an initial to a target position and a timing law so that the mobile robot can reach the ending target in a prescribed time avoiding collisions with sensed obstacles [3, 9]. From an overall point of view, solutions to the motion planning problem can be divided in two main categories

 Vito Antonio Nardi

[email protected] Valerio Scordamaglia [email protected] 1

DIIES department - via Graziella, 89124, Reggio Calabria, Italy

[10]: a) planning by modification (PBM) and b) planning by construction (PBC). PBM methods perturb a given trajectory until a set of prescribed properties is fulfilled. Such kind of solution can provide smoother trajectories at the price of solution of highly non-convex optimization problems [10, 11]. PBC methods, instead, find a trajectory by attaching new waypoints until the target is reached [12, 13] leading to trajectories tha t are typically non-smooth [14–16]. Several assumptions about operating environment (i.e. static or dynamic environment, a-priori known obstacles) may increase planning complexity [17]. Furthermore, trajectory planning algorithms are often focused on searching a trajectory taking into account geometry of the robot and its surroundings, kinematic and dynamic constraints and others that may affect the trajectory feasibility. As well-known in literature [18, 19], t