We consider obstacle localization for a team of robots cooperatively transporting a rigid payload without explicit inter-robot communication. A leader robot directs the payload's motion, while follower robots assist and react to locally detected obstacles. The leader measures the followers' aggregate wrench, i.e., the combined force and torque they exert on the payload, but cannot directly distinguish their individual reactions. We design a follower control law that allows the leader to recover obstacle locations from these measurements. Each follower resists motion toward nearby obstacles, resulting in a piecewise-linear relationship between the payload's translational and angular velocity and the aggregate wrench. Changes between adjacent linear regions reveal an obstacle's bearing and distance and identify the responding follower. We give sufficient conditions for exact recovery at a fixed payload configuration and develop an adaptive probing procedure in which the leader applies translational and rotational inputs to the payload to obtain the required measurements. We demonstrate the performance of the proposed method in simulations.
Figures & tables
Fig. 1 : The cells of twist space, which are cones, drawn where they meet a sphere centered at the origin. Each colored great circle is where one pair’s switching plane meets the sphere, and the shaded region is where one cell meets it. The black circle is the translation circle of Section IV-B , with crossings (triangles) and sample centers (circles), numbered as in Fig. 2(b) , each surrounded by its three probes (crosses, spread exaggerated for visibility). Hidden parts are faded.
Fig. 2 : (a) One probe, with the motion exaggerated: after re-centering, the payload moves out with −νp and back with νp , and the twist and wrench are recorded as it passes back near the reference position. In this illustrative probe, the payload moved 2.3 mm and turned 0.03∘ , and the return ended 3.6μ m from the reference position. (b) Payload, leader (R1), followers (R2–R5) and the six sample-center directions for n0=6 . (c) One follower’s reaction (R3) along the translation circle, zero outside the arc between its crossings (dashed).
Fig. 3 : The designed scenes at the reference pose, with the number of active pairs.
Quantity
At K1=100 N s/m
Scaling
Payload
Mass M , inertia J
2 kg, 0.5 kg m 2
–
Carrying gain μv
2 N s/m
–
Reaction
Maximum strength k
1 N s/m
–
Activation distance dact
1 m
–
Leader
Gain K2
25 N m s
K1
Probe
Speed α
3 mm/s
–
TABLE I : Parameters at K1=100 N s/m. Some of these parameters scale with K1 , with the relation shown in the last column.
K1 (N s/m)
100
1000
104
105
106
108
Pairs found / 147
54
68
83
101
120
140
False positives
3
0
0
1
0
0
TABLE II : Random scenes: pairs found and false positives at each leader gain K1 .
K1 (N s/m)
100
1000
Single (1)
1
1
Basic (2)
2
2
Crowded (4)
4
4
Double (4)
4
4
Big (6)
4
6
Total ( 17 )
15
17
TABLE III : Designed scenes: pairs found at each leader gain K1 , with no false positive.
Department of Industrial Engineering, University of Trento, Trento, Italy · Department of Information Engineering and Computer Science, University of Trento, Trento, Italy