Diseño Organizacional de los Órganos de Control

In this layer, given two configurations q_sand q_t, and stable configurations sampled at the intersections of a sequence of manifolds (i.e. the grasp manifolds of the grasp sequence {g_i}ng

i=1), the planner attempts

to generate a collision-free and stable trajectory t that connects q_sto q_tthrough these manifolds. In Alg. 1, the procedure Connect implements this process as depth-first-search. Given a current configuration qsand a sequence of grasps {gi}

ng

i=1(where g1 is the grasp in qs), the planner samples

the intersection of the first two grasp manifolds in the sequence for a set of stable configurations S (line 7). Then it tries to plan a motion from q_s to a sampled configuration q ∈ S (line 9). Note that this is a motion plan within a single manifold and thus can be solved by existing closed-chain or single- arm motion planners. However, the object motion must be also stable against gravity, for which the constrained motion planners (Berenson et al.,2011;Jaillet & Porta,2013) can be used. If the motion planning is successful, the trajectory is returned along with a recursive call to the depth-first-search. Lines 1-6 handle the simple case where q_sand q_tare already in the same manifold.

5.3

Experiments and Results

Algorithm 1 Manipulation Planning under Changing Forces

PlanStableSequence {Fi}m_i=1, q0
:

1: Go← Sample stable configurations in C and build an operation graph as shown in Fig.5.5(b)

2: qj

n

j=1← GraphSearch(Go)

3: qj

n

j=0← Insert q0to the beginning ofqj

n

j=1

4: for each subsequent qjand qj+1inqj

n j=0do

5: tj+1← PlanRegrasp(qj, qj+1)

6: if PlanRegrasp failed then

7: Go← Remove failing edge from graph Go

8: Go to line 2 9: end if 10: end for 11: return (qj n j=1,{tj} n j=1) PlanRegrasp (qs, qt):

1: Gg← Sample grasps and build graph in Fig.5.6

2: {gi} ng

i=1← GraphSearch(Gg, qs, qt)

3: t ← Connect(q_s, {g_i}ng

i=1, qt)

4: if Connect failed or t is None then

5: if maximum number of attempts reached then 6: return failure

7: end if

8: Gg← Remove failing edge from graph Gg

9: Go to line 2 10: else 11: return t 12: end if Connect q_s, {gi} ng i=1, qt
: 1: if ng= 1 then

2: t ← MotionPlan(qs, qt) using grasp gng

3: if MotionPlan successful then 4: return t 5: else 6: return failure 7: end if 8: end if 9: S ← SampleIntersection(g1, g2)

5.3 Experiments and Results

10: for each q in S do

11: t ← MotionPlan(qs, q) using grasp g1

12: if MotionPlan successful then 13: return t + Connect(q, {gi} ng i=2, qt) 14: end if 15: end for 16: return failure SampleIntersection (g, g0) :

1: One of g and g0must be bimanual. Assuming g.

2: S ← {}

3: while S contains less than k elements do 4: x ← Sample pose for object

5: q ← Solve IK with object at x and grippers at g

6: if q is stable against gravity with both g and g0then

7: Add q to S

8: end if

9: end while

10: return S

Experimental Setting:

We applied our planners to the Baxter Robot from Rethink Robotics for real robot experiments. Baxter has two 7-DOF manipulators, each equipped with a parallel plate gripper. We tested the planners in an OpenRAVE environment (Diankov & Kuffner,2008) for simulated experiments.

For Alg.1, we used the NetworkX (Hagberg et al.,2008) for graph construction and search, and BiRRT (Kuffner Jr & LaValle,2000) for motion planning. In our implementation of Alg.1, we set the maximum number of planning attempts to be 3 for the procedure PlanRegrasp and the number of samples to be 20 for the procedure SampleIntersection.

We measured the grip force/torque limits (as explained previously in Sec.4.2) of the Baxter grippers on foam boards. Specifically, along each principal axis, we applied an incremental amount of forces and torques on the foam board gripped by a Baxter gripper, to find the point when the object started to slide between the parallel gripper plates or when the object tilted more than 5odue to finger structure defor- mation. In this way, we tested the limits as f+_g,i = [13 N, 40 N, 100 N, 0.5 N m, 0.1 N m, 0.15 N m] and f−_g,i= [−13 N, −40 N, −13 N, −0.5 N m, −0.1 N m, −0.15 N m]1_.

We implemented the planners on three types of forceful operations, cutting, puncturing and drilling on rigid foam boards. We discuss how we model the operation force of these forceful operations, particularly with the existence of force deviations previously in Sec.4.1and in accordance formulate the stability check in Sec.4.2. We present a series of experiments and analysis in Sec.4.4to capture the force distributions of these forceful operations, with extracted operation models used in this chapter.

1_{Along the +z direction, the object can rest against the gripper palm, therefore the planner adopted a large force limit (100 N )}

for P+

Table 5.1: Numbers of regrasps (with standard deviations in parentheses) of three planners on three categories of tasks. Random- Puncturing V- Puncturing Drilling& Cutting Random 19.7(0.7) 52.9(10.1) 5.8(2.1) Greedy 8.2(2.1) 5.3(1.9) 3.1(0.8) Min-regrasp 5.4(1.3) 1.6(0.6) 2.0(0.5) Experiments Overview:

We conducted two categories of experimental studies, including:

– Simulated Experiments: We tested our planners on a variety of forceful tasks to verify their per- formance in minimizing the number of regrasps, planning stable regrasps and time efficiency (Sec.5.3.1);

– Real Experiments: We did a set of real human-robot experiments to further study the feasibility of our planners in the real implementations. We used a graphical user interface presented previously in Sec.4.3for task specification in these experiments (Sec.5.3.2).