Improved Continuum Joint Configuration Estimation Using a Linear Combination of Length Measurements and Optimization of Sensor Placement

Abstract

This paper presents methods for placing length sensors on a soft continuum robot joint as well as a novel configuration estimation method that drastically minimizes configuration estimation error. The methods utilized for placing sensors along the length of the joint include a single joint length sensor, sensors lined end-to-end, sensors that overlap according to a heuristic, and sensors that are placed by an optimization that we describe in this paper. The methods of configuration estimation include directly relating sensor length to a segment of the joint's angle, using an equal weighting of overlapping sensors that cover a joint segment, and using a weighted linear combination of all sensors on the continuum joint. The weights for the linear combination method are determined using robust linear regression. Using a kinematic simulation we show that placing three or more overlapping sensors and estimating the configuration with a linear combination of sensors resulted in a median error of 0.026% of the max range of motion or less. This is over a 500 times improvement as compared to using a single sensor to estimate the joint configuration. This error was computed across 80 simulated robots of different lengths and ranges of motion. We also found that the fully optimized sensor placement performed only marginally better than the placement of sensors according to the heuristic. This suggests that the use of a linear combination of sensors, with weights found using linear regression is more important than the placement of the overlapping sensors. Further, using the heuristic significantly simplifies the application of these techniques when designing for hardware.

Length Modelling of Spiral Superficial Soft Strain Sensors Using Geodesics and Covering Spaces

“…The purpose of this simulation was to verify the mathematical model of (18). It represents the soft sensor's length when attached to the surface of a toric-shaped soft actuator as mentioned earlier in Section 2.2.…”

“…Interested readers may refer to [9] for an in-depth analysis of forward and inverse kinematics. For soft actuators consisting of a single muscle, at least one sensor is required to sense the extension or bending, as it occurs across one axis only [18,19]. While for soft actuators consisting of multiple muscles, two or more sensors are required to measure the changes, as they occur across multiple axes [20,21].…”

“…The soft actuator is under bending in the XZ plane with no twist, i.e., κ > 0, φ = ψ = 0, and the soft sensor is attached vertically onto the surface, i.e., ∆v i = 0, as shown in Figure 7a,b. Substituting in (18) gives…”

Corollary discharge enables proprioception from lateral line sensory feedback

“…To fully understand the contribution of proprioceptive feedback within motor control, we must know which motor and mechanical signals are being transduced by sensors. This is an especially challenging problem for continuum joints in which shape varies continuously [ 14 ], such as that of the fish body during undulatory locomotion. While swimming, the fish’s body curvature varies from head to tail according to the phase of the motor cycle ( Fig 1A ) [ 15 ].…”

“…A fish must therefore sense and control body angles over its axial length through successive muscle layers that may span up to 10 vertebrae, rather than one or a few dedicated muscle joints [ 16 ]. In robotics, feedback from continuum joints is typically provided by sensing changes in length and curvature [ 14 ]. However, it has recently been demonstrated that stable swimming rhythms can be generated through sensing of hydrodynamic pressures on the body [ 17 ].…”