Investigations on Dynamics and Control of a Rimless Wheel based 2D Dynamic Walker using Pulsed Torque Actuation

Abstract

SYNOPSISWheeled systems are energy efficient on prepared surfaces like roads and tracks. Legged systems are capable of traversing different terrains but can be lossy. At low speeds and on off-road surfaces, legged systems using dynamic walking can be efficient. Towards this objective, the dynamics of the walker needs to be modelled and controlled. This thesis presents analysis and experiments on the dynamics and control of a rimless wheel based mobile robot (Chatur ) in a category between wheeled and legged systems. It is effectively a 2D dynamic walker that serves as a platform for investigating inverted pendulum walking. A pulsed actuation torque is proposed for the system resulting in four torque regimes defined by the ratio of energy losses to available actuator torque. Five physical constraints that limit the choice of operating points of a generic inverted pendulum walker are expounded and location of optimal operating points is discussed. Chatur's hardware design is elaborated and a control topology is proposed for pulsed actuation of the dual brushless dc (BLDC) motor driven platform with wheel synchronization.A closed-form analytical solution, using hyperbolic functions, is proposed for the stance phase inverted pendulum dynamics. Suitable models for ground impact and braking losses are used. There are four types of sub-phases within a stance phase -actuated rise, unactuated rise, actuated fall, unactuated fall. These are concatenated in four different ways to form repeating cycles yielding the four torque regimes that are identified by the fraction of stance phase for which the actuator is energized. The experimental set-up is a fixed step-angle walker built using two adjacent rimless wheels independently actuated at the hub. Varying the magnitude and duty ratio of the torque pulse, the proposed regimes are experimentally shown. The mechanical cost of transport is computed for different speeds. Videos of the walks are also taken.The operating point of an inverted pendulum walker can be specified by the combination of initial mid-stance velocity and step angle chosen for a given walk. Using basic mechanics, a framework of physical constraints that defines allowable operating points is presented. For any given speed, the optimal operating point with minimum mechanical power requirement is located based on tangency of the power and velocity contours. Repeating for different speeds, a family of optimal operating points, called the optimal locus, is obtained. Using an appropriate constant step angle over a range of speeds could lead to an inverted pendulum walker that is close to optimal.The hardware design for Chatur and the caveats associated with reliable performance of its mechanical and electrical subsystems are elaborated. In order to ensure lateral stability, the system uses two contralateral wheels driven by separate BLDC hub motors. From a motor drive perspective, the reflected load torque has a characteristic cyclic variation that repeats several times within a mechanical revolution. The proposed ...