State-Space Analysis of a Stretch3 Robot for Pick and Place

Overview

• Fixed-base industrial arms do pick-and-place precisely, but they are locked into fixed workcells and fixed capital. This project explores the flexible-automation alternative: Hello Robot's Stretch3 mobile manipulator, simulated in MuJoCo, picking and placing a cuboid and a cylinder anywhere its base can drive.
• Under the simulation sits the control theory. The lift and arm extension were modeled as a six-state state-space system, built symbolically in MATLAB and formally checked for controllability, observability, and stability, then a PD controller drove all eight degrees of freedom and an LQR took on the modeled axes to see how much performance optimal control buys.

Design & Build

• Model: Lift and arm extension as mass-spring-damper joints with first-order actuator dynamics: six states, two inputs, with the A, B, C, D matrices constructed symbolically in MATLAB from assumed numerical parameters.
• Proof: Controllability and observability matrices both computed at full rank six, every eigenvalue of A with strictly negative real part: the modeled system is controllable, observable, asymptotically stable, and BIBO stable.
• Control: A Python PD controller drives all 8 DOF of Hello Robot's Stretch3 MuJoCo model - base x and y, prismatic lift, telescopic extension, three wrist axes, and gripper - with gains tuned iteratively in the model XML.
• Benchmark: An LQR designed on the two modeled axes as a proof of concept, its Q and R weights tuned for speed, then compared head-to-head against the PD on the same step response.

Challenges

• Tuning eight joints at once: each stiffness-damping pair traded speed against overshoot, and pick-and-place punishes both the slow and the bouncy.
• Keeping the analytical model tractable - reducing eight degrees of freedom to the two that carry the pick height and reach without losing the structure worth proving things about.
• Grasping under contact: closed-loop feedback at every simulation step so the robot compensates for small disturbances and contact forces instead of fumbling the object.

Result

• Complete pick-and-place of both objects in MuJoCo with all eight degrees of freedom driven by the tuned PD controller.
• The modeled system formally shown controllable, observable, asymptotically stable, and BIBO stable in MATLAB - the analysis that argues the concept is fit to carry onto Stretch3 hardware.
• The LQR settled faster than the tuned PD at higher control aggressiveness, with a small undershoot on the lift - and MPC and hardware validation flagged as the next steps.

Skills & Tools