EK100-com: Dual Contexts in Robotics & Optical Comms

• EK100-com is a retrieval label used to index two distinct technical analyses: multi-contact feasibility in humanoid robotics and coded-modulation performance in optical communications.
• The robotics study demonstrates that arbitrary center-of-mass acceleration can be achieved if the dual friction cones intersect only at the origin, challenging conventional motion constraints.
• The optical communications research compares TTCM and BICM-LDPC, revealing a practical performance gap of about 0.4 dB at 100 Gbit/s under experimental conditions.

EK100-com is not introduced as a standardized standalone term in the cited arXiv record. The available usage instead suggests a label spanning two distinct technical contexts. One concerns humanoid motion under multiple spatially distributed contacts, where the central question is which center-of-mass (CoM) accelerations are physically feasible and when arbitrary CoM acceleration is possible (Nikolić et al., 2016). The other concerns 100 Gbit/s coherent optical transceivers, where the central question is how two coded-modulation architectures—turbo trellis-coded modulation (TTCM) and bit-interleaved coded modulation (BICM) based on LDPC codes—compare at the same net information rate, both information-theoretically and experimentally (Sillekens et al., 2016). A plausible implication is that EK100-com functions here as a retrieval label rather than a settled technical designation.

1. Scope and disambiguation

The cited literature associates EK100-com with two unrelated problem settings:

Context	Core question	Principal source
Humanoid robotics	When do multiple contacts enable arbitrary CoM acceleration, and how are feasible wrench constraints derived otherwise?	(Nikolić et al., 2016)
Coherent optical communications	How do TTCM and BICM-LDPC compare for a 100 Gbit/s transceiver at the same net spectral efficiency?	(Sillekens et al., 2016)

In the robotics usage, the object of analysis is motion feasibility under multiple point contacts with Coulomb friction and friction cones approximated by an $m$-sided pyramid. In the optical-communications usage, the object of analysis is coded-modulation performance for dual-polarization coherent transmission over a 1000 km recirculating-loop experiment using 8PSK at 28 Gbaud.

This bifurcation is not merely terminological. The first line of work studies force-generation geometry, dual cones, and linear wrench inequalities. The second studies achievable information rates (AIRs), BER, and implementation penalties under a correlated AWGN model. The commonality is methodological rather than substantive: both papers distinguish between an underlying feasibility limit and the constraints imposed by a specific practical realization.

2. Multiple-contact CoM feasibility in humanoid robotics

The robotics formulation starts from the statement that planning of any motion starts by planning the trajectory of the CoM, and that one must ensure that the robot will be able to perform the planned trajectory under the current contact configuration (Nikolić et al., 2016). The paper studies multiple spatially distributed contacts, including cases such as feet on the ground or walls and hands on walls or ceilings. Surface contacts are treated as sets of point contacts at the corners of the support polygon, and each contact force is constrained by Coulomb friction represented through a polyhedral approximation of the friction cone.

The total dynamics are written at the CoM as

$$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$

Here $m$ is mass, $\mathbf{a}$ is CoM acceleration, $\dot{\mathbf{L}}$ is angular-momentum rate, $\mathbf{F}$ is total contact force, $\mathbf{M}$ is total contact torque about the CoM, and $\mathbf{g}$ is gravity. Under this formulation, feasible CoM motion is equivalent to the existence of a feasible total wrench $(\mathbf{F},\mathbf{M})$ generated by the contacts.

For the $i$-th point contact, the friction cone is represented as

$$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$0

with generators

$$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$1

For multiple contacts, the total wrench is expressed through stacked force and torque generators,

$$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$2

where $$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$3 rotates the local contact frame to the world frame, $$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$4 is the contact point position relative to the CoM, $$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$5 is the skew-symmetric cross-product matrix, and $$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$6 contains the nonnegative cone coefficients.

The key theorem is derived using the Farkas-Minkowski theorem. A total force $$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$7 is feasible if and only if, for every vector $$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$8 satisfying

$$\begin{bmatrix} m\mathbf{a} \ \dot{\mathbf{L}} \end{bmatrix} = \begin{bmatrix} \mathbf{F} \ \mathbf{M} \end{bmatrix} + \begin{bmatrix} m\mathbf{g} \ \mathbf{0} \end{bmatrix}.$$9

it also holds that

$m$0

The paper interprets such a vector $m$1 as belonging to the intersection of the dual cones of all contact friction cones. If the only such vector is $m$2, then there is no force-direction restriction. If a nonzero $m$3 exists, then the total force space is restricted by a half-space inequality.

The exact condition for arbitrary CoM acceleration is therefore

$m$4

This means that the dual cones of all contacts intersect only at the origin. The paper emphasizes that such configurations can occur even without ground support, for example when the robot is pushing between two vertical walls. This directly addresses a common misconception that high-mobility CoM motion necessarily requires conventional ground support.

3. Detection algorithms, wrench constraint matrices, and computational behavior

To detect configurations in which arbitrary CoM acceleration is feasible, the paper proposes the linear program

$m$5

subject to

$m$6

If the optimum is

$m$7

then the dual cones intersect only at the origin, and arbitrary CoM acceleration is feasible. If

$m$8

the optimizer returns a nonzero $m$9 in the intersection of the dual cones, implying that motion is constrained (Nikolić et al., 2016).

In the constrained case, the paper derives a wrench constraint matrix (WCM), denoted $\mathbf{a}$0, such that

$\mathbf{a}$1

The derivation proceeds by rotating coordinates so that the new $\mathbf{a}$2-axis aligns with $\mathbf{a}$3, rescaling generators so that the third row becomes normalized, and expressing the wrench in a five-dimensional reduced form by dividing by the normal force component $\mathbf{a}$4. The reduced vector is

$\mathbf{a}$5

and it lies in the convex hull of points associated with the contact generators. The algorithm then computes the convex hull, extracts its bounding hyperplanes, and converts each hyperplane into a linear inequality on the wrench.

A notable computational feature is that the WCM needs to be computed only once when the contact configuration changes. If the CoM shifts from point $\mathbf{a}$6 to $\mathbf{a}$7 by $\mathbf{a}$8, then

$\mathbf{a}$9

and therefore

$\dot{\mathbf{L}}$0

This shift rule yields the same feasibility result with much less computation than recomputing from scratch.

The paper reports that the method is low-cost, with the convex-hull computation performed using Quickhull at average complexity $\dot{\mathbf{L}}$1, becoming approximately $\dot{\mathbf{L}}$2 in the stated setting. It reports WCM computation times around $\dot{\mathbf{L}}$3 ms depending on contact count and configuration, and shifted-WCM updates around $\dot{\mathbf{L}}$4 ms, reducing computation by almost two orders of magnitude. Two simulated humanoid scenarios support these claims: climbing between vertical walls, in which all examined phases satisfy $\dot{\mathbf{L}}$5, and moving sideways while hanging on top of a wall, in which the WCM is required throughout.

4. Coded-modulation architectures for 100 Gbit/s coherent optical transceivers

In the optical-communications usage, the relevant problem is an experimental comparison of two practical coded-modulation strategies for 100 Gbit/s transceivers at the same net information rate: a symbol-wise nonbinary scheme based on TTCM and a bit-wise scheme based on LDPC-coded BICM (Sillekens et al., 2016). The experiment is a dual-polarization coherent optical transmission over a recirculating loop emulating 1000 km of standard single-mode fiber.

The transmitter uses an external cavity laser at 1550 nm, an IQ Mach–Zehnder modulator driven by an arbitrary waveform generator at 28 Gbaud, dual-polarization emulation by splitting the signal into two identical single-polarization branches and recombining them with a PBS, and optional transmitter noise loading by adding ASE noise from an EDFA. The loop consists of 75 km SSMF spans, EDFA and Raman amplification, a launch power of 0 dBm per span to keep propagation effectively linear, a bandpass filter to remove out-of-band noise, and AOMs for controlling loading into the loop. At the receiver, a DP coherent receiver and standard offline DSP recover noisy 8PSK symbols. The net data rate is 100 Gbit/s, obtained from 28 Gbaud, 8PSK at 2 bit/symbol net information rate, and dual polarization. The paper also uses receiver-based noise loading by digitally adding AWGN to a received trace, enabling more precise post-FEC BER estimation than transmitter noise loading alone.

Both schemes use 8PSK with information rate 2 data bits/symbol, so the effective code rate is $\dot{\mathbf{L}}$6 and the FEC overhead is

$\dot{\mathbf{L}}$7

The main codeword length is $\dot{\mathbf{L}}$8 symbols, with a shorter case $\dot{\mathbf{L}}$9 also analyzed. The paper reports that reducing the codeword length has only a small effect in the convergence region, while LDPC gets a lower error floor with longer codewords; because the improvement from tripling the length is only modest, $\mathbf{F}$0 is adopted for the remaining results.

The TTCM implementation is based on the Robertson–Worz construction. It uses two 8-state recursive systematic convolutional encoders, both of rate $\mathbf{F}$1. The same data bits are fed to both encoders; one operates on the original 2-bit symbols, and the second operates on symbol-wise interleaved bits via $\mathbf{F}$2, after which its output is de-interleaved. Encoder outputs are punctured so that odd symbols come from one encoder and even symbols from the other, and the resulting 3-bit symbols are mapped to 8PSK using a natural binary mapping. The interleaver is random, “s-random,” and constrained so that odd positions map to odd and parallel transitions in the trellis are avoided. The decoder uses a symbol-wise soft demapper that outputs 8 log-likelihood values per received symbol, followed by two BCJR decoders exchanging only extrinsic soft information on the data bits. The decoder runs for 10 iterations, selected because this was within 0.1 dB of the best performance achieved with 100 iterations.

The BICM-LDPC implementation is based on a rate-$\mathbf{F}$3 LDPC code from DVB-S2. Input bits are serialized into three parallel streams, each two bits wide. Each stream is encoded by an identical rate-$\mathbf{F}$4 LDPC encoder; the encoded bits are then re-serialized, bit-wise interleaved, and mapped to 8PSK using binary reflected Gray coding. At the receiver, the 8PSK symbols are soft-demapped into 3 bit LLRs per symbol, which are then de-interleaved and separated into the three LDPC codewords. The LDPC decoder runs for 50 iterations, chosen so that performance was within 0.1 dB of asymptotic performance.

5. Achievable information rates, BER, and the theory–implementation gap

A major contribution of the optical paper is that it evaluates the systems using achievable information rates rather than BER alone (Sillekens et al., 2016). The channel is modeled as a multi-dimensional correlated AWGN channel,

$\mathbf{F}$5

with conditional density

$\mathbf{F}$6

and SNR defined as

$\mathbf{F}$7

For TTCM, which uses symbol-wise decoding, the AIR is the mutual information

$\mathbf{F}$8

For BICM-LDPC, which uses bit-wise decoding, the AIR is the generalized mutual information

$\mathbf{F}$9

The paper also defines post-FEC information measures. For soft-output decoding,

$\mathbf{M}$0

and for hard-output decoding,

$\mathbf{M}$1

with

$\mathbf{M}$2

The paper emphasizes that $\mathbf{M}$3 by the data processing inequality.

Experimentally, the measured BER performance matches the AWGN-based calculated performance for the implemented schemes very well, supporting the conclusion that the 1000 km transmission in the linear regime is accurately modeled by correlated AWGN. Both TTCM and LDPC show implementation penalties below 0.1 dB relative to their own ideal AWGN curves. However, when the implemented systems are compared directly, TTCM outperforms BICM-LDPC by about 0.4 dB in the 1000 km / 100 Gbit/s experiment. The paper also states that TTCM is about 0.5 dB away from its theoretical lower BER bound, whereas LDPC is about 0.8 dB away from its bound. BER measured with transmitter noise loading and receiver noise loading is consistent.

The AIR analysis clarifies why this result is not in tension with information theory. For the ideal 8PSK system at 2 bit/sym, the gap between MI and GMI is only about 0.06 dB. Thus, in the idealized comparison, the penalty of BICM-LDPC is less than 0.1 dB. The observed 0.4 dB practical gap is therefore attributed to the specific implemented codes and decoders: finite block length, iterative-decoding behavior, and implementation constraints produce additional loss, and the particular TTCM realization used in the experiment falls closer to its theoretical limit than the particular LDPC realization.

The paper further reports that near 2 bit/sym the difference between soft-decision and hard-decision outer-coding bounds is small. Around the relevant operating points—roughly 6.3 dB SNR for TTCM and roughly 6.8 dB SNR for LDPC—the hard-decision versus soft-decision difference becomes negligible, implying that a hard-decision outer code would be acceptable with only a small penalty in this regime.

6. Interpretive significance and recurring misconceptions

The two EK100-com-associated usages differ in domain but share a structural distinction between fundamental admissibility and realized performance. In the robotics case, the distinction is between contact configurations in which the intersection of dual cones is trivial, allowing arbitrary CoM acceleration, and configurations in which the motion must satisfy linear wrench inequalities encoded by the WCM (Nikolić et al., 2016). In the optical case, the distinction is between the small fundamental MI-versus-GMI gap for ideal coded modulation and the larger gap observed for specific practical TTCM and BICM-LDPC implementations (Sillekens et al., 2016).

Each paper also addresses a potential misconception. In humanoid multi-contact planning, the assumption that CoM motion is always strongly constrained by contact geometry is incomplete: the paper shows that there are configurations in which any acceleration of the CoM is feasible, even without ground support. In coded-modulation analysis, the assumption that a tiny information-theoretic gap necessarily implies nearly identical laboratory performance is also incomplete: the paper shows that practical code and decoder choices can enlarge the gap substantially.

A plausible implication is that EK100-com, in this usage, indexes technical settings where feasibility is not captured adequately by a single coarse descriptor. In one case, feasibility depends on the geometry of friction cones and their duals; in the other, performance depends jointly on AIRs, block length, iterative-decoding behavior, and the specific code family used. The cited literature therefore supports a broad reading of EK100-com as a label attached to technically precise, experimentally or algorithmically grounded feasibility analyses rather than to a single unified research topic.