Robotics Interview Prep

Waymo, Boston Dynamics, Amazon Robotics. In 2024, these companies hired hundreds of robotics engineers. Average senior robotics engineer total comp at Waymo: USD 280K. Typical onsite: 2 coding rounds, 1 math/controls round, 1 system design round, 1 ML round. This lesson is the map for all four.

• **Boston Dynamics** onsite: 7-DoF manipulator kinematics + planning for legged robot + system design for inspection robot fleet
• **Waymo L5**: perception pipeline design, sensor fusion mathematical derivation, SLAM loop closure, safety architecture
• **Amazon Robotics**: fleet coordination at scale, CBS vs ORCA trade-offs, warehouse throughput optimization

Kinematics: Forward and Inverse

A robotics engineer candidate at Boston Dynamics receives this problem: 'We have a 7-DoF manipulator. The target is (x, y, z, roll, pitch, yaw). Find the joint configuration.' This is inverse kinematics - the most common question at junior and mid-level robotics interviews.

Forward kinematics (FK): given joint configuration q, find the end-effector pose. Deterministic - always has exactly one solution. Inverse kinematics (IK): given target end-effector pose, find q. May have 0, 1, or infinitely many solutions. For redundant manipulators (DoF > 6), infinitely many solutions - the null space is exploited for obstacle avoidance and singularity avoidance.

Singularity is a configuration where the robot loses one or more DoF. Formally: the Jacobian J becomes rank-deficient. Physically: multiple joints become collinear and cannot generate motion in a particular direction. Near singularities, joint velocities approach infinity. DLS (Damped Least Squares) is the standard avoidance method: J^+ is replaced by J^T(JJ^T + lambda^2*I)^-1.

Motion Planning: From RRT to Trajectory Optimization

Waymo interview question: 'How would you plan a manipulator trajectory in a cluttered environment with 100 objects in real time?' The correct answer is not 'A*' - A* works in discrete spaces, and a 7-DoF manipulator's configuration space is continuous and 7-dimensional.

RRT (Rapidly-exploring Random Tree): samples random configurations in C-space and builds a tree of reachable configurations. Probabilistically complete (will find a solution if one exists), but not optimal. RRT* adds rewiring for asymptotic optimality. Trajectory optimization (CHOMP, TrajOpt): starts with an initial path and iteratively optimizes a functional (length + obstacle clearance). Faster than RRT if a good initial trajectory is available.

Configuration space (C-space) is the most conceptually important idea in planning. An obstacle in 3D space, when projected into C-space, becomes a C-obstacle - a region of forbidden configurations. Planning in C-space reduces the problem to finding a path in a space where a point represents the full robot configuration. This is what allows A* and RRT to apply to manipulators.

Perception Interview Questions: Kalman Filter and SLAM

Perception questions in robotics interviews fall into two types: mathematical ('explain the Kalman filter - why is it optimal?') and practical ('how do you build a map while moving with noisy sensors?'). The first tests theory knowledge, the second tests understanding of SLAM.

The Kalman filter is the optimal estimator for linear systems with Gaussian noise. Two phases: predict (update state from dynamics model) and update (correct using observation with weight inversely proportional to uncertainty). Gain K = PH^T(HPH^T + R)^-1 automatically balances trust in model vs observation. EKF linearizes nonlinear systems. UKF uses sigma points for better nonlinear approximation.

Loop closure is the key challenge in SLAM: the robot returns to a known place and must recognize it. Without loop closure, error accumulates and the map distorts. Technically: find a match between current observation and previously stored ones (bag of words, DBoW2 for visual SLAM). After match: optimize the full pose graph via bundle adjustment or pose graph optimization.

Robotics System Design: Answering Open-Ended Questions

'Design a control system for an autonomous delivery robot operating in an office building.' This question takes 45-60 minutes at senior level. The correct structure: 1) clarify requirements, 2) high-level architecture, 3) key design decisions with trade-offs, 4) failure modes and safety.

Clarifying requirements is the critical step most candidates skip. How many robots? What obstacles (people, doors, elevators)? Payload? Uptime requirement? WiFi coverage? Each answer changes the architecture. After clarification: draw a component diagram - perception -> localization -> planning -> control, plus fleet manager and cloud backend separately.

Trade-off questions are the most important part of system design interviews in robotics. Localization: pre-built map (reliable, doesn't adapt to changes) vs online SLAM (adaptive, computationally expensive). Planning: global planner (optimal, slow to replan) vs reactive (fast, gets stuck in local minima). Fleet: centralized (optimal, single point of failure) vs decentralized (resilient, suboptimal). Demonstrating knowledge of trade-offs separates senior from junior candidates.

Related Topics

Robotics interview prep brings together topics from multiple courses:

• Sensor Fusion and Kalman Filter — Mathematical questions in the perception round
• Motion Planning — RRT, PRM, trajectory optimization - core planning questions
• Robotics System Architecture — Foundation for the system design round

Key Ideas

• **Kinematics**: FK is deterministic; IK has 0/1/∞ solutions; redundant robots (7-DoF) use null space for additional optimization
• **Planning**: RRT for feasible path + shortcutting + spline smoothing; trajectory optimization (CHOMP/TrajOpt) when an initial trajectory is available
• **Perception**: Kalman Gain balances trust in model vs sensor; SLAM = graph optimization + loop closure
• **System Design**: 5 min on requirements > 40 min on architecture > demonstrate trade-offs > failure modes

Вопросы для размышления

• An interviewer asks: 'How would you localize a robot in a building without GPS?' What methods would you consider and how would you choose between them?
• For a warehouse robot fleet: what metrics would you use to evaluate fleet coordination quality? How do you measure that the algorithm is working well?
• Name three fundamentally different failure modes for an autonomous delivery robot in an office. How should the architecture handle each one?

Связанные уроки

• rob-15 — System architecture is the foundation for all interview questions
• rob-06 — Motion planning is a core interview topic
• rob-03 — Sensor fusion questions typically involve deriving the Kalman filter
• rob-12 — RL for robots appears in ML-robotics interviews at Waymo/Google
• alg-10 — Graph algorithms (A*, Dijkstra) underlie planning questions
• la-01-vectors-intro