A real-time, high fidelity dynamic simulation platform for hexapod robots on soft terrain

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Abstract

Dynamic simulation is an important aspect of legged robotic research, which is essential for its design and control. However, the dynamics of the interaction between a soft terrain and a deformable leg (e.g., a spring) is hardly taken into account. In this paper, a high-fidelity, faster-than-real-time simulation system for hexapod robots has been developed based on Vortex. Foot-terrain interaction mechanics and flexible mechanical system are taken into account in order to improve the simulation precision. A general foot-terrain interaction model is presented based on terramechanics. Pseudo-rigid-body method is used to simulate the flexibility of the robot. A speed test shows that the simulation system is capable of real-time or faster simulation. The simulation system's fidelity was validated using two hexapod robots, which is found to be greater than 90%.

Introduction

Legged robots have a number of advantages over wheeled ones, which include maneuvering through rough terrains [1], [2] and obstacles [2], [3] owning to their agile attitude adjustment [4]. Hexapod robot is an important type of legged robot dealing with heavy duty tasks. Numerous large-scale hexapod robots have been developed such as the ASV (the Adaptive Suspension Vehicle) (1986, 3.2 tons) [5], Plustech Walking Machine (1994, 3.4 tons) [6], ATHLETE (2009, 1.44 tons) [7], COMET-IV(2011, 2.12 tons), etc. [8]. In order to study the designed robot's performance and train the operator in a virtual environment, researchers have paid much attention to simulation of legged robots and developed some original platforms, such as Microsoft Robotics Development Studio (MSRDS), Webots, Gazebo and Virtual Robot Experimentation Platform (V-REP). In order to solve the contact issue between feet and terrains, numerous existing simulations such as the spring-damper model combined with Coulomb friction model [9], [12], the extended plastic collision model [13], the penalty-based method [11], and the constraint-based method [14], [15] are presented [9], [10], [11]. However, most of these platforms are based on a hard-hard contact model, and the fidelity of these contact models on deformable terrains are rarely considered [16].

Therefore, the terra-dynamics of the robot feet have been studied by researchers in recent years. Li et al. [17], [18] studied leg-ground interaction on granular medias and presented a resistive force model in 2012 and 2013. Granular flow has been studied by Kanmrin in 2012 [19], and Ding et al. presents a model of foot-terrain interaction in 2013 [20]. However, these models are limited if applied to dynamic simulation of heavy-duty robots.

Aiming for the simulation of hexapod robots, the foot-terrain interaction mechanics and the flexible mechanical system modeling method are studied in this paper. The main contributions of this paper are:

  • (1)

    A general model for the foot-terrain interaction and a method to solve its contact-area are developed. The process of lifting the foot and the influence of the tangential velocity are considered on the basis of Ding's model [20].

  • (2)

    A method for modeling and simulation of the flexible mechanical system is presented, such that the internal forces between the supporting legs are predictable, and the fidelity of the foot-terrain interaction is further improved.

  • (3)

    A high fidelity, real-time simulation system for hexapod robot is implemented based on the proposed contact model and the flexible mechanical model. The fidelity of the system is validated to be greater than 90%.

This paper is organized as follows: in Section 2, the foot-terrain interaction mechanics model and the method of mechanical system modeling is presented, which is used in the simulation. In Section 3, the simulation platform is implemented. In Section 4, speed and fidelity of the developed simulation platform are tested and validated by experiments.

Section snippets

Modeling of foot-terrain interaction

The foot-terrain mechanics is generally divided into two parts: the model in the normal direction and the model in the tangential direction. In the normal direction, the interaction force rapidly attains a maximum value when the foot starts to interact with the terrain, and then decreases to a stable value after contact, which can be simulated by the Hunt–Crossley model [20], [21]: FN=kNδn1+cNδ˙mδn2δ˙0where δ is the summation of the foot and terrain deformation, as shown in Fig. 1, cN is the

Development of the simulation system

All the calculations and modeling in this section are based on the world coordinate system Σ0, unless specifically stated. The z0 axis is set upwards in a direction opposite to gravity; the x0 and y0 axes are perpendicular to each other in the same plane, and are both perpendicular to the z0 axis. The x0, y0, and z0 axes satisfy the right hand rule.

Results and validation of the simulation system

To validate the fidelity of the proposed simulation system, simulations and experiments are done by two hexapod robots. The speed of the simulation has also been tested.

Conclusions and future work

In this paper, a simulation system for hexapod robots based on Vortex is developed. This system consists of a manipulator and control module, terrain modeling module, robot modeling module, foot-terrain interaction module, multi-rigid body dynamics module, scene displaying module and data exporting and restoring module. The following conclusions are drawn:

  • (1)

    Modeling of foot-terrain interaction mechanics for simulation of legged robots. The interaction between hard foot and hard terrain, hard

Acknowledgments

This study was supported in part by the National Natural Science Foundation of China (Grant No. 51575120/51275106), National Basic Research Program of China (Grant No. 2013CB035502), Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51521003), Foundation of Chinese State Key Laboratory of Robotics and Systems (Grant No. SKLRS201501B, SKLRS20164B, SKLRS-2013-MS-06), Harbin Talent Programme for Distinguished Young Scholars (No. 2014RFYXJ001),

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