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

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.