Dynamic Modelling and Control of an Underactuated Quasi-Omnidireccional Hexapod

Dynamic Modelling and Control of an Underactuated Quasi-Omnidireccional Hexapod

Edgar Alonso Martinez-Garcia, José A. Aguilera
DOI: 10.4018/978-1-7998-0137-5.ch016
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This chapter presents the mechanical design, dynamic model, and walking control law of an insect-like, asymmetric hexapod robot. The proposed model is an original walking mechanism designed with three actuators to provide quasi-omnidirectionality. One of the motivational aims is to reduce the number of actuators preserving similar holonomy as compared to popular 18-servo redundant hexapods with three servos per leg. This work includes the Klann mechanism as limb, two-drive differential robot's control, one per lateral triplet of legs. The legs of a triplet are synchronized in speed with different rotary angles phase. In addition, the six limbs are synchronized with bidirectional yaw motion. The proposed mechanical design has one servo for limbs yawing, one for the right limbs triplet and one motor for the left triplet. Thus, quasi-omnidirectional mobility is achieved. Furthermore, a dynamic control law that governs the robot's mechanisms motion is deduced, with an Euler-Lagrange approach. Kinematic and dynamic results are validated through numerical simulations using a tripod gait.
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Multi-legged walker robots inherently pose great locomotion capabilities due to their hype-stability over numerous complex reliefs. Some unstructured terrains include flatter, alluvial plains, farming soils, steeper, rockier uplands, watershed boundaries, drainage characterized systems and hilly terrains (HyunGyu et al., 2016). Therefore, for human safety, multi-legged walker robots are suitable to operate at dangerous landscapes where landslides, downhill creep, flows, slumps, and rock falls represent hazardous environments for humans. There exist different classes of robotic hexapods developed to perform different varieties of missions and tasks that are of great utility in field applications, Gonzalez de Santos et al. (2006). Multi-legged robots pose high steerage, which is essential to carry out missions in fields such as mining, forestry, construction, planetary exploration, vulcanography, search and rescue, demining, agriculture and so forth. Unfortunately, redundant walker robots require one rotary actuator per degree of freedom (DOF) in the joint space. Furthermore, wider physical space is required to instrument joints mechanism, besides, the electric energy consumption increases as the number of electric actuators increases too (Shekhar & Khumar, 2011), which drastically reduces the robot's operating time. Traditionally, multi-legged robots may require at least two actuators (2 DOF) to control one leg, one for azimuth rotation and another for elevation. In addition, incrementing the number of actuators to control a limb, the control models become redundantly kinematic. The number of independent variables is much greater in number than the DOF in the working space.

The work of Kazemi et al. (2013) presented the dynamics of five-link planar underactuated mechanical model of a quadruped robot with four actuated joints, its controller stabilized balance and track a desired trajectory. Kecskes et al. (2015), performed a validation study on a low-cost 18-DOF hexapod walker robot that was modeled by a 3D kinematics and dynamics model, the simulation-model realistically described the even ground contact gaits. One of our work's main contributions is the mechanical design that reduced an 18-servo model (Figure 1a) into an asymmetric three-motor underactuated version of hexapod, still preserving omnidirectional mobility (Figure 1b). In addition, a dynamic gating control law is disclosed for this type of robotic system. Haitao et al. (2016) presented a locomotion control method based on central pattern generator for hexapod walking robot to achieve gait generation with smooth transition, using a limit cycle approximation of the Van der Pol oscillator. The network governed the swing/stance phase, and locomotion control for the hexapod's leg movements during the gait cycle was developed. As a difference from our approach we control the gait speed by keep a reference torque. Knoop et al. (2017) presented a two-motor hexapod robot that walks and turn with arbitrary curvature. The walking mechanism is a modular gearbox to reciprocate sinusoidal output of continuously variable amplitude, its inputs are: a drive motor, rotating at a constant speed, and a single control input for changing the output amplitude for biomimetic robotic gaits. As a difference, our work presents two synchronization mechanisms: one for all-limb steering, and another for all-limb drive. Martinez-Garcia et al. (2014) proposed a Euler-Lagrange equation that governs the redundantly actuated legs to control the robot's displacements. Robot's rotation and translational velocities are feedback by motion estimated by optic flow of features of visual invariant descriptors. A general analytical solution of a derivative navigation law is proposed for hyper-static robots. This chapter presents a simulation framework and its physics model of an underactuated hexapod, and similarly to the present work, Roennau et al. (2015) developed an efficient and precise simulation system for multi-legged robots for experiments with the six-legged walking robot to evaluate accuracy and performance, analyze walking patterns and improve walking skills of designs of bio-inspired robots.

Key Terms in this Chapter

Passive-Joint: An articulated mechanism that transmits rotary or linear motion with no explicit actuator device, but implicitly is conducted by an actuated source of motion.

Omnidirectional Walker: A legged robot capable to move toward any directional at any time instant.

Klann-Mechanism: A seven links mechanism to produce planar cycloid motion, one joint is rotary active and Conduct motion to the other six passive links.

Quasi-Omnidirectional Walker: A multi-legged robot that can walk toward any direction taking a small latency time to adjust such a direction of motion.

Underactuated-Robot: A robot consisting of a locomotion mechanism where the number of actuators is less than the number of degrees of freedom in its working space and the inertial and gravitational forces are advantageously used.

Euler-Lagrange-Equation: A partial differential equation to find the linear generalized function of forces and angular moments of a mechanism in terms of energies and kinematic models.

Differential-Drive-Robot: A mobile robot that has steering control by varying two lateral drives. Dynamic Control: A mathematical model that considers together kinematics and kinetics to form an equation with non-stationary control transition matrix.

Synchronized Limbs: A multi-legged robot that steer all limbs simultaneously toward a same direction and speeds are the same, regardless of the motion phases.

Asymmetric-Hexapod: A six-legged robotic platform where all limbs distances between their locations and the robot’s geometric center are not equal.

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