Sensor Observability Analysis for Maximizing Task-Space Observability of Articulated Robots

TL;DR

This paper introduces Sensor Observability Analysis (SOA), a framework to quantify how well distributed directional sensors observe task-space axes for articulated robots. By rotating local sensor axes into the task frame, applying a sensor transformation, and aggregating into a sensor observability matrix $S$ and system vector $s$, it defines a scalar observability index $o$ and an observability ellipsoid to reveal configurations that blind certain axes. The authors compare SOA to traditional kinematic manipulability, show its advantages for non-traditional sensor placements, and provide methods to maximize observability via null-space projections or a quadratic programming formulation, including axis-specific targets and sensor-threshold handling. They validate the approach with simulations and physical experiments on a custom 3-DOF robot and the Baxter robot, demonstrating that observability singularities degrade force sensing but can be mitigated by reconfiguring sensor viewpoints. The work lays groundwork for sensor-aware design, planning, and control in compliant and interactive robotic tasks, with extensions to non-joint-mounted sensors and more complex architectures in future work.

Abstract

We propose a novel performance metric for articulated robots with distributed directional sensors called the sensor observability analysis (SOA). These robot-mounted distributed directional sensors (e.g., joint torque sensors) change their individual sensing directions as the joints move. SOA transforms individual sensors axes in joint space to provide the cumulative sensing quality of these sensors to observe each task-space axis, akin to forward kinematics for sensors. For example, certain joint configurations may align joint torque sensors in such a way that they are unable to observe interaction forces in one or more task-space axes. The resultant sensor observability performance metrics can then be used in optimization and in null-space control to avoid sensor observability singular configurations or to maximize sensor observability in particular directions. We use the specific case of force sensing in serial robot manipulators to showcase the analysis. Parallels are drawn between sensor observability and the traditional kinematic manipulability; SOA is shown to be more generalizable in terms of analysing non-joint-mounted sensors and can potentially be applied to sensor types other than for force sensing. Simulations and experiments using a custom 3-DOF robot and the Baxter robot demonstrate the utility and importance of sensor observability in physical interactions.

Figures (11)

• Figure 1: Comparison of a) joint axes $\bm{\hat{z}}_k$ and kinematic manipulability $w_k$ and b) positioning of joint-mounted and link-mounted sensors $\bm{\hat{s}}^i$ and the sensor observability $o$ and their respective ellipsoids for the same robot configuration.
• Figure 2: a) Representation of a single 7-DOF Baxter robot arm with only traditional joint torque sensors in b) arbitrary configuration, c) kinematic singularity in $\theta_z$, d-e) sensor observability singularities in d) $\tau_x$ and e) $f_x$. Force and torque observability ellipsoids based on the sum function $\Gamma_{sum}(\cdot)$ are shown in red dashed and blue solid ellipsoids, respectively. Note that the ellipsoids in c) are very thin, but not completely flat, i.e. $o \neq 0$.
• Figure 3: a) Simulation of a single Baxter robot arm starting in an arbitrary position, sweeping through an observability singularity at $t = 4$ s (configuration shown in Fig. \ref{['fig:robotconfig-singsensX']}), setting joints $\bm{q}_{2}$ to $\bm{q}_{6}$ to 0 at $t = 8$ s, and ending in an arbitrary position at $t = 12$ s. b) Joint positions of the maneuver. Joint $q_7$ is not shown as it is held at a constant $q_7 = 0$. c) Plot of the evolution of kinematic manipulability $w_k$ and observability index using the sum $o_{sum}$ and max $o_{max}$ functions. All indices are normalized to 1, but $w_k$ is further scaled with an exponential to emphasize the changes at $t = 4$ s.
• Figure 4: Sensor observability experiments using the robot Baxter comparing end effector forces estimated by the joint torque sensors and measured using an external force sensor attached to the end effector in a) an arbitrary non-zero observability configuration and b) the observability singular configuration shown in Fig. \ref{['fig:robotconfig-singsensX']}. An external force is applied first in $x$, then $y$, and finally $x$ again. Forces are fully observable in the arbitrary position in a), but forces in $x$ are not observable in the observability singular configuration in b).
• Figure 5: Configuration where a non-zero null space vector exists for $\bm{J}^T$, but it is not a sensor observability singularity as $o \neq 0$. This configuration is similar to Fig. \ref{['fig:robotconfig-singsensX']} but $q_6$ tilts the end effector is slightly downwards.