Shape space planner for shape-accelerated balancing mobile robots

Abstract

Abstract-This paper introduces shape-accelerated balancing systems as a special class of underactuated systems wherein their shape configurations can be mapped to the accelerations in the position space. These systems are destabilized by gravitational forces and have non-integrable constraints on their dynamics. Balancing mobile robots, like the ballbot, are examples of such systems. The ballbot is a human-sized dynamically stable mobile robot that balances on a single ball. This paper presents a shape trajectory planner that uses dynamic constraint equations to plan trajectories in the shape space, which when tracked will result in approximate tracking of desired position trajectories. The planner can handle systems with more shape variables than position variables, and can also handle cases where a subset of the shape variables is artificially constrained. Experimental results are shown on the ballbot with arms where different desired position space motions are achieved by tracking shape space motions of either body lean angles, or arm angles or combinations of the two; and also by tracking only the body lean motions while the arm angles are artificially constrained.

Full-body collision detection and reaction with omnidirectional mobile platforms: a step towards safe human–robot interaction

“…Other sensing properties have been used for contact interactions, notably the tilt measured by an inertial measurement unit on ball-bot robots [18]. This type of robot, and the associated inertial sensing, have been used effectively to handle contact interactions with people [14].…”

“…Push recovery in humanoid robots allows them to regain balance by stepping in the direction of the push [20] or quickly crouching down [25]. Inherently unstable robots like ball-bots [18,14] and Segways [19] have been able to easily recover from pushes and collisions using inertial sensor data. A four-wheel robotic base with azimuth joint torque sensors [7] has been able to respond to human push interactions, but only when its wheels are properly aligned with respect to direction of the collision.…”

Learning of closed-loop motion control

“…However, motion planning on ballbots has not yet been thoroughly addressed. Nagarajan et al [11] use a separated trajectory planning and tracking controller to generate a set of motion primitives which are later connected to one trajectory by a graph search algorithm. In another approach Shomin et al [12] suggest a differentially flat representation of the system dynamics to generate trajectories.…”

Dynamically Feasible Motion Planning through Partial Differential Flatness.

“…Partial differential flatness can also be compared with shape-accelerated underactuated balancing systems as defined in [15], wherein the configuration space is equally partitioned into unactuated shape variables and actuated position variables. However, in [15], trajectory tracking is performed by considering a position trajectory, and inverting the non-holonomic dynamic constraint between the acceleration of the position variables and the shape variables and their higher order derivatives, under the assumption that the shape variables are constant. This results in a shape variable trajectory point-wise in time.…”

“…We will also briefly note the similarities / differences / relations between our notion of partial differential flatness and relative flatness [19], defect of a nonlinear system [6], shapeaccelerated underactuated balancing systems [15], and partial feedback linearization [20].…”