is to perform tracking and assume that the configuration
between the needle and the manipulator tip is known and
remains unchanged over time [18]. Then the robot Jacobian
and joint-sensor readings are used to estimate the motions
of the needle. However, getting to this known state is
nontrivial, as grasping a needle itself is a non-deterministic
action, and grasp pose is situation-dependent, such as during
regrasping [8]. Thus, the work in [19] does not assume a
known configuration of the needle held by an end-effector,
and its motions are estimated by a tool-tracking method [7]
that tracks the pose of the end-effector. These approaches
take into account that the needle should move concurrently
with the gripper when held by it. Nonetheless, they do not
ensure that the suture needle pose lies inside the feasible
grasping manifold of the gripper.
Tracking the poses of an in-hand needle is a constrained
pose tracking problem, where the needle should always
lie inside the feasible grasping manifold of the gripper.
However, there is no unified approach to define a feasible
grasping manifold since grippers and grasped objects can
be in arbitrary shapes, making this task highly nonlinear. To
incorporate constraints into nonlinear tracking problems, pre-
vious work follow two approaches: acceptance/rejection sam-
pling [20] and optimization [21], [22]. Acceptance/rejection
methods are known to reduce the diversity of the tracked
pose [22] and require an excessive number of feasibility
checks, making them not desirable for real-time track-
ing [23]. On the other hand, optimization methods project
the estimated pose onto a feasible manifold. However, they
require the manifold to be defined as equality or inequality
constraints [22], [23], and describing the feasible grasping
manifold in such a way would be highly nontrivial.
B. Contributions
In this work, we achieve state-of-the-art performance
for real-time suture needle tracking in robotic surgery by
incorporating grasping constraints. To this end, we present
the following novel contributions:
1) the first approach to probabilistically track a suture
needle in real-time with grasping constraints,
2) a state-space to describe a grasped suture needle for
efficient sampling on the feasible grasping manifold,
3) and a comparison of Bayesian filter approaches that
incorporate the grasping constraints.
The proposed methods are evaluated in both simulation
and real-world environments. In simulation environments, we
demonstrate that our proposed methods outperform other un-
constrained/constrained tracking approaches. Moreover, we
evaluate different tracking methods on the suture needle re-
grasping task [8], [9]. The results indicate that incorporating
grasping constraints makes the regrasping policy more robust
to noise in detections. In real-world environments, we use
marker-less feature detections from a Deep Neural Network
(DNN) as needle observations and reconstruct the tracked
tool poses from ex-vivo images. An example is shown in
Fig. 1. The results demonstrate that our constrained approach
ensures a feasible estimated pose, and an unconstrained
method can lead to unrealistic reconstructions.
II. METHODS
A. Problem Formulation
We aim to solve the in-hand suture needle pose, st,
tracking problem probabilistically from a sequence of ob-
servations, o0:t, which can be formulated as:
Track pt|t(st):=p(st|a0:t−1,o0:t)
s.t. st∈ Ft
where st=f(st−1,at−1,wt−1)∼pf(·|st−1,at−1)
ot=h(st,vt)∼ph(·|st)
(1)
where Ftis the feasible grasping space, f(·)and h(·)are
the motion and observation models with noise wt−1and vt
respectively, and at−1is the action applied to the suture
needle.
In our task, Ftin (1) is the feasible grasping manifold
of the surgical manipulator that is holding a suture needle at
time step t. Usually, a grasping manifold should consider two
feasibility constraints: geometric and dynamic constraints.
Geometric constraints include [24]:
1) The object’s surface should be in contact with the
gripper’s surface, i.e., Surface(st)∩Surface(et)6=∅,
where etis the state of the gripper at time step t.
2) The object should not penetrate with the gripper, i.e.,
Interior(st)∩Interior(et) = ∅.
Dynamic constraints include that if there is no external force
except gravity acting on both the object and the gripper,
the linear and angular velocities of the object relative to the
gripper should be 0. Hence, the feasible grasping manifold
Ftcan be represented as
Ft={st|st∈ Gt∩ Dt},(2)
where Gt={st|Surface(st)∩Surface(et)6=∅and
Interior(st)∩Interior(et) = ∅},(3)
Dt={st|If ExternalF orce \Gravity =∅,
LinearV elocity(st,et) = 0and
AngularV elocity(st,et) = 0}.(4)
Due to the special design and property of surgical manipu-
lators and suture needles, we can simplify the requirements
of defining the feasible grasping manifold for an in-hand
needle. More specifically, the dynamic constraints in (4) are
ignored because (1) a suture needle is very light compared
to the gripper, and (2) grippers for surgical manipulators
are designed to increase the friction between themselves and
the objects they are holding (e.g., Needle Drivers). Hence,
Ft=Gt,∀t∈[1, . . . , T ].
Since the robot end-effector or the grasped object can have
a complex shape, the feasible grasping manifold Ftin (2) is
difficult to define for the object pose, [b>
tq>
t]>, where bt∈
R3is the position, and qt∈R3is the axis-angle orientation.
The object pose, which is described in a global frame such as
the camera frame or in the ego-centric end-effector frame,