IEEE Robotics & Automation Magazine - June 2021 - 78

The initial path generated
by the harmonic maps
technique is optimized with
respect to minimization
of trajectory execution
time, obstacle avoidance,
and compliance with
kinodynamic constraints
such as satisfying input
and state constraints.
maximum opening, length, and height to calculate the optimal
grasping area, as shown in Figure 5. This methodology is
decoupled from the machine learning-based object
detection algorithm due
to the real-time feedback
requirements during the
reach-to-grasp phase.
Moreover, when the robot
is approaching the detected
object, the object's point
cloud noise acquired by the
sensor is reduced, and its
density is increased, making
the aforementioned
analytical methodology
suitable for robust and reliable
real-time grasping
regions computation.
The decentralized
motion planning and
control solution for the
automated load exchange
task among heterogeneous
robots is described
in a recent study [17].
More precisely, a motion
planning algorithm based on probabilistic road maps calculates
a connected graph G. This graph consists of feasible
configurations for the robotic system-which is holding the
object to be loaded on a mobile platform-to facilitate the
Grasping Algorithm Pseudocode
Require: The visible object's point cloud and gripper geometrical
characteristics (maxOpening, height).
1: procedure GRASPALGORITHM (maxOpening, height)
2: while algorithm_enabled do
3:
4:
5:
6:
7:
8:
9:
10:
11:
loading procedure, given the workspace constraints, its
structure limitations, and the geometric characteristics of
the mobile platform. The robotic system follows a feasible
trajectory generated by a pathfinding algorithm employed
on the computed graph G [Figure 6(a)]. Meanwhile, the
mobile platform moves autonomously toward the object
using the motion control scheme as described in the " Navigation "
section. When the mobile platform reaches the
loading area, the object is successfully placed on it. The previous
presented method [17] is extended for three agents (a
static manipulator, a mobile manipulator, and a mobile
platform). Initially, the mobile manipulator and static
manipulator are cooperatively grasping the object. Then,
the mobile manipulator, acting as the leader, calculates a
graph G, consisting of connected feasible loading configurations
of the object, taking into account the system limitations
(i.e., static manipulator workspace limitations,
obstacles, mobile platform's geometrical characteristics).
Then, it calculates the optimal one and, performing a pathfinding
algorithm, computes a feasible path that connects
the initial object configuration with the desired one. Finally,
the mobile manipulator leads the way to cooperatively
transport the object with the static manipulator in a decentralized
fashion by following the calculated path [Figure
6(b)]. The decentralized cooperative manipulation
methodology is described in the following paragraphs.
A leader-follower decentralized scheme is implemented
for the cooperative object manipulation tasks. The follower is
charged with the estimation of the desired trajectory utilizing
a prescribed performance estimator following a similar
ObjectPoints ← GetObjectVisiblePoints()
ObjectPose ← GetObjectPose()
if size(ObjectPoints) > 0 then
(b)
ObjectPoints ← TransformPoints(ObjectPoints, ObjectPose)
contour ← ConcaveHullContour(ObjectPoints)
graspZone ← GraspableZone(contour, maxOpening)
ORg, Opg ← OptimalGrasp(graspZone, height)
CRg, Cpg ← TransformPoint (gpO, ObjectPose)
return CRg, Cpg
(a)
Figure 5. The optimal (a) grasping algorithm, (b) object detection, and (c) grasping area.
78 * IEEE ROBOTICS & AUTOMATION MAGAZINE * JUNE 2021
Calculated Grasping Area
{O}
opg, oRg
(c)
IEEE Robotics & Automation Magazine - June 2021

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